PARIS — From airports and government offices to company boardrooms and stock exchange floors, turmoil and anger spread across Europe on Thursday after President Trump abruptly blocked most visitors from the Continent to the United States to curb the spread of the coronavirus.

Mr. Trump’s 30-day travel ban, announced in a prime-time address Wednesday evening while most Europeans were asleep, began causing shock waves even before the sun rose across the Continent. In the hours that followed, the ban sent stocks tanking and tempers rising across European capitals.

In a strongly worded statement, the European Union said it “disapproves of the fact that the U.S. decision to impose a travel ban was taken unilaterally and without consultation.’’ It said that it was “taking strong action to limit the spread’’ of the coronavirus, but that it “is a global crisis, not limited to any continent and it requires cooperation rather than unilateral action.’’

In the predawn hours, initial confusion over the details of the restrictions — they take effect late Friday in the United States — sent many travelers scrambling for fear that they would not be allowed into the United States. The rules apply to people who have been in Europe’s 26-country, passport-free zone over the previous 14 days, though not to Americans or permanent U.S. residents.