Among other conditions, Turkey insists that any agreement advance its hopes of joining the bloc.

BRUSSELS — European Union leaders said early Tuesday they reached the outlines for a possible deal with Ankara to return thousands of migrants to Turkey and said they were confident a full agreement could be reached at a summit next week.

During 12 hours of negotiations, Turkey insisted that any agreement would require Europe to advance Turkey’s long-delayed hope of joining the bloc.

Turkey also said it expects EU nations to ease its visa restrictions on Turkish citizens within months.

Turkey said it would be willing to make greater efforts to contain irregular migration. “This is a welcome approach,” German Chancellor Angela Merkel said, but added “it needs more time” for the member states to fully approve it.

British Prime Minister David Cameron said that “we do have the basis for a breakthrough, which is the possibility that in the future all migrants who arrive in Greece will be returned to Turkey.” The sides will now reconvene at a two-day summit starting March 17.

Turkey, home to 2.75 million refugees chiefly from neighboring Syria, surprised EU counterparts Monday by demanding a doubling of funding beyond the $3.3 billion already pledged. “Turkey is ready to work with the EU, and Turkey is ready to be a member of the EU as well,” Turkish Prime Minister Ahmet Davatoglu told reporters.

For its part, the EU sought to gain stronger commitments from Turkey to take back refugees who have reached European shores and ease a crisis that has left an estimated 13,000 to 14,000 people encamped in the wintry cold on the Greece-Macedonia border.

“To stop refugees arriving in Greece, we have to cooperate with Turkey,” French President Francois Hollande said. Even though many saw the outlines of a deal, it was still too early to clinch it.

In Ankara, the Turkish capital, President Recep Tayyip Erdogan accused the EU of failing to provide enough of the already pledged funds. He also criticized Europe for refusing to accept asylum seekers more readily, linking that policy to needless deaths as thousands opt to cross illegally by sea from the Turkish coast to offshore Greek islands.

“We are not sending them. They are going by sea and many of them are dying. We have rescued close to 100,000 from the sea,” Erdogan said in a speech.

Turkey is seeking a new EU commitment to take Syrians and other refugee applicants via safe travel routes, such as at the land border between Turkey and Greece, to reduce drowning deaths in the Aegean Sea.

Overshadowing the summit diplomacy is Turkey’s questionable human rights record. On Friday, Turkish police stormed the headquarters of an anti-government newspaper to enforce a court order placing the paper and its sister outlets under new management.