WASHINGTON—President Trump declared a national emergency over the coronavirus pandemic, a move that he said would free up billions in assistance to states and give him additional authority as the rapidly spreading virus upends life across the country.

Mr. Trump, speaking in the White House’s Rose Garden on Friday, said the national emergency declaration would open up access to up to $50 billion in financial assistance for states, localities and territories. He also called on every U.S. state to immediately set up emergency...