In New York City, despite its many major hospitals and research institutions, only about 55 coronavirus cases a day on average last month were sequenced and screened for more contagious variants.

That amounted to just 1 percent of the city’s new cases, a rate far below the 10 percent that some experts say is needed to understand the dynamics of New York’s epidemic at a time when more contagious variants, including some that may blunt the effectiveness of existing vaccines, have led to surges of cases in Britain, Brazil and South Africa.

By the end of February, New York City health officials hope to have a more robust surveillance program in place that would involve sequencing the genomes — that is, examining the genetic material for mutations — of about 10 percent of new virus cases, according to Dr. Jay Varma, a senior public health adviser to City Hall.

With an average of more than 5,000 new cases a day in recent weeks, that would provide a good picture of which variants are present in New York and how widely they are proliferating, Dr. Varma said.

But the effort to reach that benchmark is underscoring how, a year into the pandemic, local, state and federal officials have often been slow to mobilize resources for public health needs.

“Trying to get laboratories that are primarily focused on things like human genome sequencing specifically for cancer or other conditions to shift their interest to work on pathogens sometimes takes effort,” he said.

The capacity to sequence the genomes of as many virus samples as necessary already exists, scattered across the city, though it has been largely untapped.

“Every institution is doing their own thing,” said Professor Adriana Heguy of New York University’s Grossman School of Medicine, whose team has been sequencing some 96 samples a week and whose research last year helped establish that New York’s epidemic arrived via Europe, not China.

In the past few weeks, City Hall aides have been asking a number of research scientists and laboratory directors across the city to commit to sequencing far more coronavirus samples than they have been doing so far, and to uploading the results to an online database, according to interviews. On Monday, more than 90 cases were sequenced at a single laboratory — a significant increase.

“The scientific community cannot really organize without an overarching architecture,” Professor Heguy said. “The city is really now trying to organize this and it’s the right thing to do.”

Until recently, the expectation has been that coronavirus cases will drop as vaccinations proceed. But if one of the more contagious variants starts circulating widely in New York City, it may cause a new wave of cases that overshadows the second wave that New York is still fighting off, according to public health experts and a modeling team at N.Y.U.

It is not yet known which trajectory New York is on, or is headed for, and that is largely because of a lack of genomic surveillance. The new variants may be starting to gain a foothold in New York, or they may not: Finding that out would only require regular sequencing of enough new virus cases.

One of these variants, first identified in Britain and known as B.1.1.7, was detected in 13 cases in New York City in January, according to figures provided by the city’s health department. They were identified out of some 1,703 specimens from the city that had been sequenced in January, according to the department.

What percentage of virus cases should be sequenced is a matter of debate. Britain is currently sequencing up to 10 percent of new cases, while the rate in the United States was well below one percent several weeks ago.

“In my opinion, we should be doing 10 to 15 percent,” Professor Heguy said.

Dr. Varma said the city’s goal of 10 percent came from Britain’s success in quickly identifying the variant and tracking its spread.

With its major academic medical centers and research institutions, there are far more sequencing machines in New York than would be needed to check the coronavirus genomes from every positive case, were anybody inclined to do so.

“Our machines could handle thousands or hundreds of thousands,” said Dr. Neville Sanjana, a scientist with a lab at the New York Genome Center in Lower Manhattan. “So the capacity is just not the issue.”

The issue for research laboratories — strangely enough, amid a pandemic that has probably infected more than a quarter of New Yorkers — is access to samples. In New York, there is no high-volume pipeline of positive virus samples from hospitals or testing sites to research laboratories to conduct genetic surveillance.

“It’s really just organizing that sample collection — that, I think, is what’s missing,” said Dr. Sanjana, whose research has involved searching for which medicines might block infection by inhibiting the human genes that the coronavirus hijacks.

What is needed, scientists said in interviews, is for the city or another entity to essentially bifurcate the current coronavirus testing process. Each day, tens of thousands of New Yorkers provide swabbed samples, which are generally sent to a few large laboratories for testing. If those labs could set aside a portion of the samples, those portions could later be used for genome sequencing if they turned out to be positive.

“It’s solvable, but it needs resources and it needs people to coordinate,” Professor Heguy said, as she listed the necessary steps: A portion of the original sample would need to be set aside; RNA would need to be isolated from it; and someone would need to transport the RNA samples to a laboratory that does genome sequencing.

The city’s goal of expanding sequencing at least tenfold will require enlisting a range of outside laboratories and research projects, big and small. The city anticipates that the largest share of the genomic sequencing will happen at a laboratory in Long Island City, Queens, that is run by a small robotics company.

The company, Opentrons, also runs a facility in Manhattan called the Pandemic Response Laboratory. That laboratory was built last year to help the city solve the testing crisis that emerged during the summer, when big commercial laboratories were struggling to handle the soaring caseload. People were having to wait several days, and sometimes a week or two, for coronavirus test results. The laboratory now tests 20,000 samples a day.

Will Canine, a co-founder of Opentrons, said that a courier will regularly drive RNA samples prepared at the Pandemic Response Laboratory to the company's facility in Queens where they will be sequenced.

The laboratory is aiming to sequence as many as 2,000 of its positive samples each week by mid-February, charging the city less than $75 for each sample sequenced, company officials said.

Additionally, the city is encouraging a range of other institutions, including a number of hospitals, medical schools and research institutions, to sequence more samples.

Few places have as much capacity as the New York Genome Center, where dozens of machines are often used for research projects that might involve sequencing the genomes of many people to search for specific genes underlying a certain illness.

Sequencing the coronavirus genome is a far smaller undertaking, given that the human genome is about 100,000 times longer.

One scientist at the Genome Center, Michael Zody, said the center was trying to work through obstacles, such as access to samples and how to quickly prepare a large number of samples for the sequencing machines.

“Right now, we’re still actively trying to scale up,” he said.

One of the first, and most surprising, additions to the city’s surveillance effort involves a day care center that Rockefeller University opened to enable scientists to return to work last year.

The university, a biomedical research institution on Manhattan’s Upper East Side, has five Nobel Prize winners on its faculty and a century ago was deeply engaged in the response to the 1918 influenza pandemic. So perhaps it is of little surprise that the day care center is playing a role in scientific research.

Scientists there had been working on a high-sensitivity saliva test, which allowed for easier testing of infants and toddlers who often object to a nasal swab. And recently, the university has begun sequencing the positive coronavirus cases to see if the child may have been infected by one of the more contagious variants.

In a way, the infants and toddlers dropped off each day have become sentinels for the entire city.

“We just started doing this,” Dr. Robert Darnell of Rockefeller University said last week. “We’ve sequenced about 15 so far.”