The Delta surge appears to have peaked in Florida and other states that drove the most recent Covid-19 surge, offering some relief after the variant upended what many thought would be a more normal summer.

But cases and hospitalizations have been rising in many other states including Kentucky and North Carolina, data show, and public-health experts said the return of unvaccinated schoolchildren to classrooms, cold weather in Northern states and the holiday season could yet give the virus new opportunities to spread.

“I don’t know if we’ve peaked for all time, but the wave that was currently ongoing seems to have crested and is falling in some states but is rising in others,” said Andrew Noymer, an infectious disease epidemiologist and demographer at the University of California, Irvine.

The highly contagious Delta variant fueled a rapid increase in cases, often in places where vaccination rates have lagged behind the national average. By Saturday, before the long holiday weekend slowed data reporting, the U.S. was adding about 164,000 new Covid-19 cases a day, according to a seven-day average compiled from Johns Hopkins University data. The average had dipped below 12,000 in June, the data show.

Some states where cases surged most dramatically appear to be experiencing a break in the storm. Arkansas, Mississippi and Missouri have recently been adding new cases at a slower clip than in July, for example. The national seven-day average of new Covid-19 hospital admissions has ticked downward since late August, according to federal data.

And the Covid-19 swell in Florida, where Delta pushed cases to their highest-ever levels and led Florida to contribute more to the summer surge than any other state, also shows signs of easing.

Deaths, a lagging indicator, are at record-high levels due to the recent case and hospitalization surges. But the state’s most recent weekly report showed about 129,000 new cases in the week that began Aug. 27, down nearly 15% from the prior week. This was the first significant decline after weekly case totals had leveled off for about three weeks following a steep climb.

“There are some good indications that things are starting to look better in Florida,” said Mary Jo Trepka, an infectious disease epidemiologist at Florida International University who tracks the trajectory of the virus in the state.

Rising hospitalizations might have encouraged some people to take more precautions to avoid catching or spreading the disease, she and other researchers said. In July and August, vaccination rates rose in many states that were hard-hit by the variant. The growing combination of people with some level of Covid-19 immune response from prior infection or vaccination has also contributed to the slowdown, said Dr. Trepka.

She cautioned, however, that Florida’s cases and hospitalizations might still trend upward again in the coming weeks and months. “I don’t think we’ve had the fallout yet with the schools,” Dr. Trepka said.

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Because Florida accounted for about one in five cases at one point during the most recent surge, its Covid-19 decline and declines in other hard-hit states are slowing the Delta surge nationally. Whether cases will start to trend lower soon nationally is difficult to project, in part due to lags in reporting after the Labor Day weekend.

But the effects of the surge are far from over, infectious disease epidemiologists said. The seven-day average for newly reported U.S. deaths recently topped 1,500 a day, exceeding peaks during a smaller surge in cases in the summer of 2020, and are likely to keep rising while catching up to cases.

Louisville, Ky., schools have been testing students to try to combat rising case numbers.

Photo: Jon Cherry/Getty Images

Some public-health experts say they believe the U.K.’s experience with Covid-19 cases during its Delta-fueled wave is reason for caution. The seven-day average in U.K. cases in July plummeted from a peak of around 48,000 cases a day to under 26,000 later that month, only to start climbing again. By late last month the average had reached about 35,000, national data show.

Cases in some U.S. states, including Kentucky and West Virginia, have recently been on the upswing, threatening to mute the effect of declines in Florida and elsewhere. Cases are also rising in parts of the Midwest. More than 40 states have recently had higher seven-day averages than 14-day averages, Johns Hopkins data show, an indicator that cases are on the rise.

“What was in the South is now going to spread due north and then west,” said Peter Hotez, dean of the National School of Tropical Medicine at Baylor College of Medicine.

In Tennessee, new hospital admissions are up almost 11% from the prior week to an average of more than 400 admissions a day, federal data show, surpassing the peak of the winter surge. In Davidson County, home to Nashville, active cases jumped from 444 on July 2 to 5,700 on Sept. 1. Hospitalizations are rising too.

“I think the wave that hit Florida, Arkansas and others, we’re just starting to see it,” said Alex Jahangir, an orthopedic surgeon and chair of the Covid-19 task force in Nashville.

One question, health experts said, is how cold-weather states with above-average vaccination rates, like those in New England, will fare as people escape the cold. Federal data show more than 66% of people in Massachusetts are fully vaccinated, trailing only Vermont and Connecticut, and far ahead of the 53.2% national level. New England States also top the 62.3% national level for eligible people who are fully vaccinated.

These vaccination rates will likely help blunt the impact of the virus, infectious-disease experts say. But that is not a guarantee: A recent Covid-19 surge in Oregon, also among the better-vaccinated states, shows how Delta can easily find and exploit populations who still aren’t protected against the disease.

“The most important thing we can do to mitigate that is to convince as many people as possible to get vaccinated,” said Daniel Kuritzkes, chief of the infectious-diseases division at Brigham and Women’s Hospital in Boston.

Cars lined up for services at a Covid-19 testing and vaccination site in Nashville, Tenn., Sept. 1.

Photo: USA TODAY NETWORK via Reuters Co

Write to Jon Kamp at jon.kamp@wsj.com, Brianna Abbott at brianna.abbott@wsj.com and Anthony DeBarros at Anthony.Debarros@wsj.com