President Donald Trump and Vice President Mike Pence said they see signs the U.S. coronavirus outbreak is beginning to level off or stabilize, citing a day-to-day reduction in deaths in New York, the COVID-19 epicenter in the country.

“We’re beginning to see the glimmers of progress,” Pence said at a White House news conference on Sunday. “The experts will tell me not to jump to any conclusions, and I’m not, but like your president I’m an optimistic person.”

Pence said the government is starting to see “cases and most importantly losses” beginning to stabilize.

New York state reported 594 new coronavirus deaths on Sunday, a reduction of 36 from Saturday. Governor Andrew Cuomo said in a daily briefing that the data may show the state is reaching a “plateau” -- or could be “just a blip.”

But Trump was more optimistic. “Maybe that’s a good sign,” he said. “We hope we’re seeing a leveling off.”

The U.S. has the largest publicly reported coronavirus outbreak in the world, with more than 335,000 cases and more than 9,500 deaths so far, according to Johns Hopkins University. Trump said Saturday that the country faces “a very, very deadly period” over the next two weeks.

Trump said the latest numbers on the outbreak had changed the White House’s projections of how many Americans may die, but he didn’t elaborate. Last week, the White House projected that between 100,000 and 240,000 people would die in the outbreak.

Deborah Birx, the State Department immunologist who has directed the White House’s projections, said that an “independent” model she had examined over the weekend still projected about 100,000 U.S. deaths. She said that Italy and Spain, which together have had more than 260,000 cases and more than 28,000 deaths, have “crossed the apex” of their outbreaks after aggressive social distancing efforts for the past four weeks.

“That’s our word to the American people, that we can look like that,” she said.