WASHINGTON—President Trump announced a 30-day ban on some travel from Europe into the U.S. and said he would act to offer financial assistance to those affected by the coronavirus pandemic rapidly spreading across the country and around the world.

Mr. Trump, in a national address from the Oval Office on Wednesday, said the travel suspension would begin Friday at 11:59 p.m. and would exclude the U.K. He suggested the restrictions would also apply to cargo, but the White House later said they applied only to people and declined to answer other questions.

“The restriction stops people not goods,” Mr. Trump later tweeted.

Hours after the address, the State Department advised U.S. citizens against all travel abroad, even to countries not yet experiencing an outbreak. The department warned of mandatory quarantines, travel restrictions and other measures that could complicate international travel.

The virus has spread to more than 100 countries, roiled markets and disrupted daily life across the country and around the world. The sober address marked Mr. Trump’s most direct response to date, though he again tried to sound an optimistic note and defended actions already taken by his administration.