BRUSSELS—British Prime Minister David Cameron said Tuesday that the U.K. wouldn't be able to enjoy all the benefits of European Union membership without having to pay any of the costs, as he began the tortuous process of extricating his country from the EU.

He met leaders of the other 27 EU states for the first time since last Thursday's historic referendum, telling them that migration would be a key issue determining their future relationship. He said the EU should be flexible on its principle of free movement if it wants to maintain a close economic relationship with Britain.

"Of course it's a sad night for me because I didn't want to be in this position," Mr. Cameron said. But he said he was more concerned about Britain "getting its relationship right with Europe." He said he would do everything he can do encourage a close relationship between Britain and the EU. "That will involve compromises," he said.

Mr. Cameron, who announced after the referendum that he would resign within a few months, didn't set out specific proposals for the U.K.'s future relationship with the bloc during the meeting. He said the tone of the discussion was positive and constructive.

Write to Jenny Gross at jenny.gross@wsj.com

(END) Dow Jones Newswires

June 28, 2016 21:25 ET (01:25 GMT)