WASHINGTON—President Trump on Sunday said he was extending the administration’s social-distancing guidelines for another 30 days through the end of April, after saying for days that he was hoping to open up the country in the coming weeks.

Mr. Trump, speaking at a news conference in the White House Rose Garden, said the peak of the death rate from the new coronavirus was expected to hit in two weeks. Mr. Trump predicted the country would be on its way to recovery by June 1.

“Nothing...