BRUSSELS — The European Union on Thursday lashed out at President Donald Trump’s “unilateral” decision to restrict travel from Europe to the United States over the coronavirus, saying that the illness does not respect borders.

Trump announced that all European travel would be cut off, but U.S. officials later clarified that restrictions would apply only to most foreign citizens who have been in Europe’s passport-free travel zone at any point for 14 days prior to their arrival to the United States.

“The European Union disapproves of the fact that the U.S. decision to impose a travel ban was taken unilaterally and without consultation,” EU Council President Charles Michel and Commission President Ursula von der Leyen said in a joint statement.

“The coronavirus is a global crisis, not limited to any continent and it requires cooperation rather than unilateral action,” the two said.

They rejected Trump’s suggestion that Europe is not doing enough to combat COVID-19, saying that the 27-nation bloc “is taking strong action to limit the spread of the virus.”

The so-called Schengen area comprises 26 countries including EU members France, Italy, German, Greece, Austria and Belgium, where the bloc has its headquarters, but also others like Switzerland, Norway and Iceland.

The restrictions announced by Trump don’t apply to the United Kingdom, where the number of confirmed cases has reached 460, or Ireland, which isn’t part of Schengen.

According to the European Centre for Disease Prevention and Control’s latest figures, more than 17,000 cases of COVID-19 have been confirmed across Europe, and more than 700 people have died on the continent.

For most people, the new coronavirus causes only mild or moderate symptoms, such as fever and cough. For some, especially older adults and people with existing health problems, it can cause more severe illness, including pneumonia. The vast majority of people recover from the new virus.

With the virus now present in all 27 EU countries, the bloc’s top officials have pledged to stand united in fighting the disease and are likely to adopt a common approach in their response to Trump’s announcement.

This week, von der Leyen announced the launch of a “corona response investment fund” seeded with 7.5 billion euros that she said would reap billions more. It’s aimed at propping up health care structures, small businesses suffering from the impact of the virus and labor markets where jobs might be hit.

Von der Leyen postponed a trip Thursday to Greece to discuss the migrant stand-off with Turkey in order to focus on combating the rapid spread of the virus.

Several EU meetings have been cancelled to slow the spread, but the bloc’s interior ministers are still scheduled to gather in Brussels on Friday. EU health ministers were holding a video-conference later Thursday.

As the virus spreads, more European countries are adopting drastic measures. After Italy entered a lockdown, Denmark said all schools and day-care facilities in the country will be closed from Monday. All public servants who don’t perform critical functions, have been ordered to stay home for the next two weeks.

Meanwhile, the U.S. Army decided to cut down the number of troops taking part in massive war games that have been planned across Europe over the next six months because of the virus pandemic.

The Defender-Europe 2020 exercises were set to involve around 20,000 American personnel, the biggest deployment of U.S. troops to Europe in the last 25 years.

But U.S. Army Europe said “in light of the current coronavirus outbreak, we will modify the exercise by reducing the number of U.S. participants.” No details on numbers were provided.