Nearly four months after the pandemic’s peak, New York City is facing such serious delays in returning coronavirus test results that public health experts are warning that the problems could hinder efforts to reopen the local economy and schools.

Despite repeated pledges from Gov. Andrew M. Cuomo and Mayor Bill de Blasio that testing would be both widely accessible and effective, thousands of New Yorkers have had to wait a week or more for results, and at some clinics the median wait time is nine days. One prominent local official has even proposed the drastic step of limiting testing.

The delays in New York City are caused in part by the outbreak’s spike in states like California, Florida and Texas, which has strained laboratories across the country and touched off a renewed national testing crisis.

But officials have also been unable to adequately expand the capacity of state and city government laboratories in New York to test rapidly at a time when they are asking more New Yorkers to get tested to guard against a second wave.

The delays limit the ability of public health officials to quickly identify — and isolate — people who are infected while also diminishing the usefulness of New York City’s contact-tracing program. They also can lead to growing blind spots that obscure the extent of the virus’s spread, which could spell trouble as the city tries to reopen.

As a result, some public officials and laboratory executives say New York’s strategy of allowing anyone and everyone who wants a test to get one is unsustainable.

“I’m afraid that we have to prioritize people with symptoms, someone who has been exposed, or someone whose work puts them in contact with a lot of people,” said a city councilman, Mark Levine, a Manhattan Democrat who heads the Council’s health committee. “That’s what I’m about to call for, but I don’t think City Hall wants to.”

New York was once the epicenter of the pandemic in the United States, suffering more than 30,000 deaths, far more than any other state. But by shutting down in March and April, it has significantly slowed the spread of the virus. The Northeast has emerged as the only region in the country to beat back the outbreak.

When the pandemic peaked in the city, testing was relatively scarce, and prominent elected officials, from President Trump to Mr. Cuomo and Mr. de Blasio, said they would ensure that in the future, there would be more than enough.

As capacity expanded, New York City authorities began encouraging everyone to get tested, and urged people to get tested repeatedly, setting a target of 50,000 tests per day.

In recent weeks, about 20,000 to 35,000 people are tested most weekdays, a demand that has put a strain on local labs.

City public health officials said they were growing increasingly alarmed by the delays, pointing out that widespread testing and quick turnaround times were needed to reduce transmission by asymptomatic and pre-symptomatic patients, who are believed to play a major part in the virus’s spread.

“This is becoming a problem,” said Dr. Jay Varma, a City Hall adviser who has a critical role in the city’s testing and contact-tracing program. “Any lag in this process can make it more difficult to have case and contact tracing be effective.”

Still, Gareth Rhodes, an aide to Mr. Cuomo and a member of his virus response team, said that there was a priority placed on tests for people with Covid-19 symptoms and those who reported being exposed to someone who is positive for the virus. He added that some labs could return such tests in less than 24 hours.

But if someone has no symptoms and no known exposure, he said, “I’m less concerned if the result comes back in five, six, seven days.”

Mr. de Blasio said on Thursday that he was moving to address delays in testing. He blamed the national surge in cases for the waits and said labs were overwhelmed.

Asked how delays were able to mount in New York City after the mayor pledged to prioritize testing, Mr. de Blasio said the city had to “reset the equation” after cases spiked across the country.

“I’ve been consistent — we want fast turnaround times and we want the maximum number of people tested, and that has been working overwhelmingly until we hit this glitch,” the mayor told reporters.

On Thursday, the governor defended the state’s performance, noting that longer delays were being seen because some heavily used labs were “getting overwhelmed” by demand for results from other states.

New York processes about 70 percent of its tests at a network of more than 200 private labs, which the state has enlisted to process specimens, Mr. Cuomo said. It was redirecting some samples to underutilized facilities, he added, which resulted in average wait times for results from those labs of 2.6 days.

But Mr. Cuomo conceded that some samples sent to busy national labs had wait times that averaged six to 10 days, and sometimes even longer.

And the governor said the problems could get even worse in the fall, during flu season, when labs would be asked to process samples looking for that infection. “The flu tests will eat at the capacity,” he said.

New York City is finding ways to lessen its reliance on commercial laboratories, like Quest Diagnostics, where backlogs sometimes mean waits of up to two weeks. The city’s Department of Health and Mental Hygiene is vowing to expand its own capacity to conduct tests.

But the delays may get worse before they get better. The reasons are complex, but are largely driven by a simple fact: Demand for coronavirus tests has grown faster than laboratory capacity. And demand is likely to increase with the start of the school year, particularly with some universities requiring the tests for students.

“The pressure put on us by the higher-ed community, who wants every kid to have a negative test to show up on campus, will soon put a strain on the testing system,” said Scott J. Becker, the chief executive of the Association of Public Health Laboratories.

The current crisis carries some echoes of February and March, when limited testing capacity and a disastrous series of missteps by the federal government meant relatively few sick New Yorkers were able to get tested. The virus spread rapidly — and largely undetected.

The nation’s testing capacity has expanded significantly since then. More than 750,000 tests are administered across the nation on some days.

But even as laboratories try to increase capacity, some supplies are getting more difficult to obtain. In particular, the cartridges that have been critical for quick testing at many hospitals are growing scarcer, said Dr. Dwayne Breining, who oversees laboratories at Northwell Health, New York’s largest hospital system.

“There are effects in our area from what’s going on in the rest of the country,” he said. “All of those companies are kind of allocating their supply to the places that are hot spots, which is clinically appropriate.”

As of early July, results for about a quarter of coronavirus tests in New York City were returned within 24 hours, a mayoral spokeswoman, Avery Cohen, said. But a quarter of tests took more than six days, she said.

Some of the longest delays are at the dozens of CityMD walk-in clinics that have blanketed the city in recent years. Thousands of New Yorkers seek tests there each day.

CityMD sends many coronavirus tests to a Quest Diagnostics laboratory in Teterboro, N.J., for processing. Quest Diagnostics has cited a range of factors for why turnaround times have been doubling or tripling, including the growing number of orders from employees returning to work and from hospitals that have resumed elective surgeries, but need first to screen patients.

“We’re not taking specimens from southern parts of the country and moving those to the Teterboro, New Jersey, lab,” Wendy Bost, a spokeswoman for Quest Diagnostics, said. “The Teterboro lab is dealing with volume that is coming from the region.”

Across the nation, test results on average take slightly more than two days for priority samples, Quest Diagnostics said. But for everyone else, the wait times have been getting much longer — up two weeks in some instances.

Some other laboratories have managed to keep turnaround times shorter. The city’s public hospital system, which runs a network of health clinics and community testing sites, sends many samples to BioReference Laboratories, which currently has a turnaround time of two to three days for nonpriority samples, said Dr. Jon R. Cohen, executive chairman of BioReference, one of the nation’s largest commercial laboratories.

BioReference is using a “pooling” technique, where if a batch tests negative, all the samples are deemed negative. If it tests positive, each sample must be individually tested.

For now, City Hall’s strategy for reducing turnaround times has been to advertise free testing at city-run sites, where the waits tend to be shorter, city officials said.

The Health Department is also working on transforming nine clinics that had been used to test and treat patients for sexually transmitted diseases and tuberculosis into coronavirus testing sites. That would expand the city’s public laboratory capacity considerably.

The health commissioner, Dr. Oxiris Barbot, said these sites would be able to process “a couple of thousand tests a day.”

Stories of long waits for results have become common among New Yorkers.

Lee Ziesche, 31, said she went to get a virus test on July 5 at a CityMD location in her Brooklyn neighborhood, Bedford-Stuyvesant, as a precaution after her boyfriend’s roommate started feeling sick. She said she got her results on July 20.

“I wasn’t that worried about myself, but the reflection on how the system is working was super concerning,” she said. “It makes it really hard for us to return to normal when it takes two weeks for us to get tests.”

Zach Honig, 34, who lives in the Financial District, said he was tested on July 12 in anticipation of a trip to Maine and still had not gotten his results.

“Honestly, I don’t even really see the point in getting tested,” he said. “Even if I get a positive result, I imagine I wouldn’t even be contagious anymore. It’s just not really practical.”

So far, the delays do not seem to have contributed to an uptick of transmission, but a second wave of the outbreak looms.

“That seriously undermines the entire purpose of testing — both to inform people they are contagious so they are quarantined and also to trigger the contact tracing to find out who else may have been exposed,” Mr. Levine, the councilman, said. “With a delay of seven days, you can be pretty certain the virus will spread.”

Dr. Varma, the City Hall adviser, said it would be a mistake to restrict testing to only the symptomatic. Despite the lag times, he said, it made sense “to push through and stick with your strategy of expanding testing as much as possible.”

Testing and contact tracing are tightly linked: After people with active virus infections are discovered through testing, contact tracers interview them about whom they in turn may have infected. Then contact tracers try to get these contacts into quarantine before they become contagious.

The longer test results take, the more likely contact tracers will simply be tracking the spread of the virus from person to person, rather than stopping it, said Charles King, an AIDS activist, and member of a City Hall appointed group advising the contact-tracing program.

“Frankly, if you can’t get results within 24 hours,” Mr. King said, “you do start losing the utility of the exercise.”

Emma G. Fitzsimmons and Troy Closson contributed reporting.