President Donald Trump, seizing on recent signs of progress in hard-hit areas like Seattle and New York City, has said coronavirus cases in the U.S. have peaked, suggesting that the worst of the pandemic is over as he encourages states to ease up on restrictions and revive an economy in tailspin.

“The battle continues, but the data suggests that nationwide we have passed the peak on new cases. Hopefully that will continue and we will continue to make great progress,” Trump said Wednesday at the White House.

In the same news conference, he added, “It looks like we’re plateauing and maybe even, in many cases, coming down.””Our experts say the curve has flattened and the peak in new cases is behind us,” he said Thursday.

But experts told NBC News that Trump’s claims of a plateau are premature or exaggerated.

“He’s claiming to have knowledge on something it’s impossible for him” to know, said Dr. Vin Gupta, a pulmonologist, global health policy expert and an NBC News and MSNBC contributor. “You need to test the country broadly to really know if the [COVID-19] cases are down.”

Gupta said the best data the U.S. has is in-hospital deaths due to COVID-19, because people are able to get tested more easily when they are hospitalized. The data on confirmed infections nationwide is likely a sizable undercount, because any people who are asymptomatic or who have mild symptoms are not getting tested.

Full coverage of the coronavirus outbreak

“What we feel confident on, via statistical models, the number of people dying in hospitals from COVID has stabilized,” Gupta said.

But there’s no way to know whether actual infections are down without widespread testing.

Home deaths add more uncertainty to the data, too, he said, noting that New York City has begun revising death tolls to include those likely related to coronavirus. There have been at least 7,890 confirmed coronavirus-related fatalities in the five boroughs and another 4,309 “probable” COVID-19 deaths as of Friday afternoon., according to the city’s daily tally.

Experts urged caution in overstating successes, saying that a relaxing of social distancing — and the reopening of businesses where people congregate — could undermine the success in controlling the spread and trigger a second surge.

“We haven’t seen anything that indicates we are at the tail end of the outbreak,” said Joseph Fair, a virologist, epidemiologist and NBC News and MSNBC contributor. “We want to be farther down the downslope.”

Fair said the president’s claims of a plateau are likely accurate for areas with strict social distancing measures, like New York City.

But with unrestricted travel between states and different stay-at-home policies in different states, Fair said the U.S. is playing a “whack-a-mole game” rather than truly controlling the outbreak.

“New York City goes down, but then Houston pops up,” he said. “I think we have plateaued in certain places… I don’t think we’ve plateaued everywhere.”

Download the NBC News app for full coverage of the coronavirus outbreak

Indeed, areas that were initially not hard hit are now preparing for their own surges.

Rhode Island Gov. Gina Raimondo said Friday the state is preparing for a peak in two weeks, as the state’s hospitalizations and fatalities continue to rise. South Dakota Gov. Kristi Noem said Sioux Falls’ peak would hit in the middle of May, after a meat processing plant in the area became a hotspot for the virus. Officials from Mecklenburg County, North Carolina — which includes the city of Charlotte — said their peak could hit June 25.

Fair said caution is important when analyzing data because incubation periods can mask transmission rates.

“Historical precedents teach us that infectious disease comes in waves,” he said. “We try not to put too much into five good days, because that could be people coming through incubation