Facing an alarming increase in pro athletes testing positive for the coronavirus, along with the rest of the country, the N.B.A. announced Sunday that it would postpone five games, bringing to seven the total number of coronavirus-related postponements in the N.B.A. this season.

Also on Sunday, the N.H.L. announced that “due to the concern about cross-border travel and, given the fluid nature of federal travel restrictions,” it would postpone 21 games slated for Monday through Dec. 23 and which pitted Canadian against U.S.-based teams. Those games are scheduled to resume on Dec. 27.

And the N.F.L. and N.F.L. Players Association on Saturday made a change to its testing protocols, the fourth such adjustment in a week.

They were the latest amendments to schedules and health rules pro leagues have made in lieu of stopping their seasons. With high vaccination rates among players and staff members, both the N.F.L. and N.B.A. have generally scaled back Covid-19 testing, which aligns with guidance from the Centers for Disease Control. According to the C.D.C., vaccinated individuals do not need to be tested unless they are exposed or show symptoms, advice that pro leagues seem to be embracing after previously testing with more frequency.

In a memo to all 32 teams sent Saturday, Commissioner Roger Goodell said that players will be given test kits that they can use at home to help them “identify and self-report a possible infection before entering the facility.”

Vaccinated N.F.L. players who are asymptomatic will be subject to “strategic and targeted” tests, while players who report symptoms of a coronavirus infection will be tested “promptly.”

The N.F.L.’s testing strategy mirrors other pro leagues, though the N.BA. and N.H.L. temporarily instituted daily testing measures for players, regardless of vaccination status, amid the current surge fueled by the Omicron variant: N.B.A. players will be tested daily for two weeks starting Dec. 26, and N.H.L. players began testing on Saturday and will continue until at least Jan. 1.

“I would not describe it as, we’re stopping testing” for vaccinated players, Dr. Allen Sills, the N.F.L.’s chief medical officer, said Saturday on a call with reporters. “We’re trying to test smarter and in a more strategic fashion.”

Those decisions to rely on the self-reporting of symptoms raised fresh questions about whether players will do so and face the prospect of missing a start if they test positive. It’s worked in other sectors of society, said Dr. Amesh Adalja, a senior scholar at the Johns Hopkins Center for Health Security at the Bloomberg School of Public Health. Hospitals, for instance, have relied on the honor code and most do not test vaccinated employees weekly, in line with guidance from the Centers for Disease Control. Dr. Adalja said sports leagues could also introduce other measures, like spot testing or symptom screening, to augment other testing.

“I think that the N.F.L. players and the coaches have to be professional and know that they don’t want to be putting other people at risk,” Adalja said. “They shouldn’t be playing sick, but that’s obviously going to be as good as the honesty of the people there.”

The players union has pushed for daily testing for all players, as the league required in 2020, with N.F.L.P.A. president J.C. Tretter writing in a September 2021 post to the union’s website that merely testing vaccinated players weekly could allow virus transmission inside team facilities for a dangerously long window.

Goodell’s memo Saturday came on the heels of a bevy of Covid-19 protocol changes the N.F.L. made in a week in which it was forced to postpone three of this weekend’s games, the first such delays this season.

Facing a single-day high in players’ positive tests Monday, the league mandated booster shots for team staff members who work most closely with players. On Thursday, after more than 100 players tested positive over the week, the league reinstituted mandatory mask-wearing inside team facilities and restrictions on in-person gatherings. More than 130 players were placed on N.F.L. teams’ Covid-19/reserve lists this week, including at least 10 from the Los Angeles Rams, Cleveland Browns and Washington Football Team.

With the spike in positive cases threatening the weekend’s slate of games, the N.F.L. also changed its policies to allow options for fully vaccinated players who tested positive to become active more quickly, provided they are asymptomatic for at least 24 hours. Now those players may return from quarantine as soon as the day after their initial positive test.

On Saturday, the N.H.L. announced strengthened protocols that include daily testing for all members of a club’s traveling party. Players and coaches are prohibited from eating indoors at restaurants and bars, and are encouraged to wear masks indoors.

A joint statement from the league and the N.H.L.P.A. released Sunday said that after meetings with medical experts, the season would continue amid the postponements; so far 39 games will be rescheduled. The need to temporarily shut down individual teams would continue to be made on a case-by-case basis.

The statement also said that the league and players’ union are “actively discussing the matter” of the N.H.L.’s participation in the upcoming Olympics in Beijing and expect to “announce a final determination in the coming days.”

In England, the Premier League canceled nearly all of their matches this weekend because teams were overrun with positive cases.

Coronavirus cases have risen despite the high vaccination rates among players in pro sports. About 95 percent of N.F.L. players are vaccinated, according to the league. That far exceeds the rest of the country, where 72 percent of people ages 18 and up have been vaccinated. But it slightly trails other sports leagues — only one N.H.L. player is unvaccinated and 97 percent of N.B.A. players have been inoculated. Because of the high vaccination rates, Adalja said daily testing for the inoculated is not necessary. That type of surveillance picks up cases that are “not very clinically significant,” because the infected are mostly asymptomatic or show mild symptoms.

“We’re going to have Covid cases in the N.F.L. 20 years from now — they’re going to still be occurring,” Adalja said. “I think we have to think about what we’re trying to achieve.”

Adalja expects the virus to become endemic and recommends that health officials in every arena put their efforts into navigating a reality in which the virus is a part of daily life. He added that, in that scenario, everyday testing would not be valuable.

The N.F.L. did not mandate that its players be vaccinated, but relaxed its Covid-19 protocols and restrictions ahead of this season for those who did get inoculated, lifting mitigation guidelines like mask-wearing and decreasing the frequency of testing.

But with the uptick in positive cases, pro football has reinstated many of the 2020 policies that helped the league complete its entire regular season and postseason slate according to schedule, with only daily testing remaining the difference.

The relaxation of protocols highlights the choice sports leagues and other companies must make at this stage of the pandemic. Dr. Vin Gupta, a pulmonologist and a professor at the University of Washington who has advised the Seattle Seahawks on Covid-19 issues, said he has sensed a desire among organizations to scale back mitigation measures to return to some sense of normalcy. Gupta said each entity will have to evaluate its tolerance for positive tests in an era in which vaccines offer strong protection against severe illness.

“We’re coming up at this at a pivot point, and I think Omicron’s going to accelerate this, where we have to accept a new normal and a new risk paradigm,” Gupta said in an interview last week.

“For the last 22 months, it’s been a positive test, test, trace, isolate,” Gupta added. “I think we’re going to start normalizing toward what we can actually scale from a solution standpoint that is going to keep people out of the hospital. I bet that is what the N.F.L. is going to shoot for.”