BRUSSELS — The leaders of the European Union gathered on Saturday in Brussels without Prime Minister Theresa May of Britain to finalize their negotiating strategy as the prospect of the end of more than four decades of British membership in the bloc drew closer.
The summit meeting is the first of its kind at which 27 leaders will take binding decisions in a slimmed down format, minus Britain and Mrs. May.
The leaders, including Chancellor Angela Merkel of Germany and President François Hollande of France, are expected to endorse a tough strategy on negotiating Britain’s exit, or “Brexit,” that could eventually force the government in London to make politically awkward choices.
The idea is to force Britain to reach a deal on the terms of its divorce before starting talks on relations after it leaves the bloc.
Donald Tusk, the president of the European Council, the body that represents bloc’s leaders, told reporters ahead of the summit meeting, “Before discussing the future, we must sort out our past.” He added, “That is the only possible way to move forward.”
One of the thorniest issues is getting Britain to guarantee that the three million citizens of other European Union nations who are living in Britain and the 1.2 million Britons living in the European Union can maintain their residency rights and other entitlements.
The leaders are also likely to call on Britain to meets its outstanding financial obligations so that other member states can avoid paying higher costs after the British withdrawal. The outstanding bill could amount to as much as €60 billion. But British citizens and politicians are balking at paying such a large sum.
Another key issue: pushing Britain to maintain a free flow of trade and people between Northern Ireland, which will leave the bloc with Britain, and the Republic of Ireland, which will remain a full member of the European Union.
Britain is expected to be reminded to abide by the terms of the 1998 Good Friday Agreement, including keeping the door open to the possible unification of Ireland.
In March, Mrs. May formally started the two-year process of leaving the European Union, and the weekend gathering in Brussels is the logical consequence of that step, taken after a majority of the British electorate voted for Brexit 10 months ago.
Yet, Mrs. May is confronting European leaders who are more optimistic about their joint future than they have been in several years.
European leaders are emboldened by mostly positive economic news in recent months and by the defeats of ferocious opponents of the bloc in elections in Austria and the Netherlands. The Europeans are also broadly optimistic that Emmanuel Macron, the centrist candidate in the French presidential elections, will prevail over Marine Le Pen of the far-right National Front in the final round on May 7.
The demand that Britain first make sufficient progress on assuring the rights of citizens of other member nations, on settling its bill and on safeguarding Irish peace and prosperity before talking about a trade deal amounts to a blow for Mrs. May. But it seems unlikely to dent her chances of being re-elected in a snap election she called for June 8 in order to have a stronger mandate in Brexit negotiations.
Even so, Britain badly needs a trade deal, or a transitional arrangement, to avoid facing barriers to the 440 million European Union consumers who are the biggest buyers of exports from the United Kingdom after it leaves the bloc, as soon as 2019.
Although Mrs. May has backed away from suggestions that her country could simply walk away without a trade deal, Mrs. Merkel has warned that some in Britain still had “illusions” about what the nation stood to gain during the two-year negotiations.
Mrs. May has since accused European countries of preparing to “line up to oppose us.”
The gathering in Brussels comes after a conference of the 27 leaders in March to sign the Rome Declaration confirming their commitment to integrating the Continent even as a series of crises has badly weakened integration efforts.
Much is at stake for the countries remaining in the bloc. They must overcome their habitual squabbling and balance their desire to keep trade and military ties with Britain while ensuring that it does not enjoy the same benefits as a member of the bloc, such as unfettered access to the vast European Union single market.
They are also wary of Britain turning itself into a low-tax haven with weakened regulations that would undercut European neighbors.
Unwinding the 44-year relationship between London and Brussels is fiendishly complicated. Britain is the first country to leave, and the procedure for the separation, known as Article 50, had never before been used.
Michel Barnier, the main European Union negotiator, said he wanted to wrap up talks by October 2018 to enable the European Parliament and member states to assess the results.
“We need to remain united as the E.U. 27,” Mr. Tusk said on Saturday. “It is only then that we will be able to conclude the negotiations,” he said.