European leaders have also noted President Trump’s lack of enthusiasm for NATO and other multilateral institutions, and they have apparently decided, as Chancellor Angela Merkel of Germany said in May, that “the era in which we could fully rely on others is over to some extent,” and that “we Europeans truly have to take our fate into our own hands.”

Ms. Merkel did add, however, that European coordination should be taken in partnership with the United States and Britain.

For years, Britain blocked this kind of cooperation, concerned that the creation of a European army would undermine NATO and London’s alliance with Washington. Britain instead favored a bilateral arrangement with France.

But with Britain having voted to leave the European Union, a process known as Brexit, the other countries in the bloc — especially France, Germany, Italy and Spain — saw the long-dormant idea of military cooperation as a way to show their citizens that Brussels could respond to worries about security and terrorism.

Paris had argued for a smaller group of countries that would commit to serious spending on military equipment and capabilities, which Europe mostly lacks outside of NATO, while Berlin argued for a bigger club. France, which will become the most important military power in the European Union after Britain departs, wants to be able to conduct operations in places like Mali with European allies without necessarily having to ask NATO for help.