After a spike in positive tests for the coronavirus among players this week, the N.F.L. said in a memo that it would mandate booster shots for team staff members who work most closely with players.

Even with a vaccination rate among players that is over 94 percent, more coronavirus cases have been reported this season in the N.F.L. compared with last year, according to a review of league data by The New York Times. The sense of urgency escalated Monday, when 37 players tested positive, the highest single-day total since the start of the pandemic.

The N.F.L. said the players’ positive tests were being driven by community spread, though the number of coronavirus cases across the United States, while rising, is still below 2020 levels. According to N.F.L. data, 360 players and team staff members tested positive from August to mid-November, a 33 percent increase compared with the 270 cases detected over the same time in 2020.

There have also been high-profile positives, from Green Bay Packers quarterback Aaron Rodgers, the league’s reigning most valuable player, who misled interviewers about his vaccination status and was fined in November for not following virus protocols; and Tampa Bay Buccaneers receiver Antonio Brown, who in December was suspended by the league for presenting a fake vaccination record.

In its memo to all 32 teams sent on Monday, the N.F.L. ordered coaches and team employees who work directly with players to receive booster shots by Dec. 27 or be relegated to noncontact roles “to ensure that we continue to reduce risk of transmission and allow us to complete the N.F.L. season safely during the pandemic.”

But the N.F.L. Players Association said the rise in cases was cause to return to daily testing for everyone, regardless of vaccination status. Fully inoculated players and team staff members are now tested once a week, and more if they are deemed a close contact or show symptoms. By contrast, unvaccinated players are required to test daily and restricted in when they can use training rooms, how they are allowed to travel to games and the size of the groups in which they can congregate while away from the team.

In the 2020 season, all players and essential personnel were tested every day, a part of the safety regimen N.F.L. medical experts said was critical in enabling the league to contain outbreaks and to complete all 256 regular-season games and a full postseason while much of the country was under restrictions.

The persistence of cases has forced the N.F.L. and its players to adjust, and readjust, pandemic protocols while reopening a debate between the league and its players’ union over the frequency of testing for the virus.

When Covid-19 vaccines became widely available in the spring, the N.F.L. relaxed some of its safety protocols, such as masking, social distancing and daily testing, for team employees who were vaccinated and required they be tested every two weeks.

The rollback on testing drew objections from the union, which negotiates with the league on workplace conditions, this summer as the Delta variant emerged. The union encouraged its membership to get vaccinations to reduce the chance of severe illness, and expressed a preference to return to daily testing but in August reluctantly agreed to a weekly testing cadence.

“If you keep the virus out of the building, then you can assure that it’s not being spread in the building,” Dr. Thom Mayer, the union’s medical director, said in an interview.

Mayer warned that, under the league’s current guidelines, which are enforced by the teams, an infected, asymptomatic vaccinated person could walk around a facility unmasked for days before the virus was detected.

The Seattle Seahawks have imposed extra protections since very early in the pandemic. A team spokesman said the organization was testing vaccinated players and staff twice a week instead of just once. So far this season, only one of its players has been on the Covid-19 list and in the 2020 season it was the only club to not report an infection.

The league reinstated a mask mandate inside team buildings from Nov. 25 and Dec. 1, and required that all players, coaches and support staff also must be tested for the coronavirus on Nov. 29 and Dec. 1, after the Thanksgiving weekend when potential exposures at holiday gatherings were expected to be high. The N.F.L.’s testing data showed that case counts continued to rise during the final two weeks of November, but the rate of increase slowed. Multiple members of the league’s medical team said the current case counts do not indicate a need to return to daily testing.

“The goal isn’t to test as much as you can,” said Dr. Christina Mack, who is an epidemiologist, vice president at the health care data science company IQVIA, and an adviser to the league. “The goal is to set up a comprehensive program to keep people safe and to detect infection when it’s there in a strategic way.”

Mayer, the union’s medical director, disagreed.

“You can’t intervene in the face of what you know about the virus unless you know what the virus is doing,” he said.

Dr. Allen Sills, the N.F.L.’s chief medical officer, said in an interview on Nov. 30 that the rise in cases this season needs to be examined and responded to in context of the current landscape.

The N.F.L. collects real-time data from testing, contact tracing and genomic sequencing, essentially virus fingerprinting that enables scientists to spot variants and map out chains of transmission. The genomic sequencing, Sills said, indicates that in the majority of cases, transmission took place in the outside community, not the highly vaccinated team population.

“We don’t think Covid Zero is an achievable goal,” he said, especially with players and their families interacting with the outside world more than they did last season, when stay-at-home orders limited movement. The mission now, Sills said, is avoiding outbreaks, severe disease and cardiac complications.

“I think that our story this year has shown that while we will still have positive tests, we’re not seeing the same disease burden that we saw in 2020,” he said

The N.F.L.’s testing showed that vaccinated players who test positive have tended to have milder and shorter illnesses — with approximately 20 percent testing out of isolation before 10 days, the league said. Unvaccinated players must quarantine for at least 10 days if they test positive, while the vaccinated may return when they produce two negative tests 24 hours apart.

Dr. Michael Osterholm, an epidemiologist at University of Minnesota and league consultant who served on President Biden’s Covid-19 advisory board, along with other medical experts who review the N.F.L.’s data weekly, said so far they believe the current protocols are sufficient to contain coronavirus spread. When cases or exposures arise, clubs temporarily follow a set of stricter protocols, which require more remote meetings, masking and daily testing for all personnel, regardless of vaccination status.

“I can say with certain certainty that the N.F.L. has not de-emphasized the importance of Covid,” Osterholm said.