BRUSSELS—British Prime Minister David Cameron moved closer to finding an agreement with the European Union’s other 27 leaders to reset the U.K.’s relationship with the bloc, after working through the night to hash out differences, but there were still unresolved issues early Friday morning.

A British official said there was difficult work ahead.

“It’s hard going,” the official said, after Mr. Cameron left the EU summit after 5:30 a.m. “Some signs of progress but nothing yet agreed and still a lot to do.”

Mr. Cameron on Friday hopes to secure a deal in an agreement that would pave the way for a referendum in the U.K. on Britain’s EU membership in late June, capping nine months of discussions with EU leaders.

Early Friday, he met with European Council President Donald Tusk and French President François Hollande.

Negotiations will continue later Friday on concessions he wants from the bloc, including on issues related to sovereignty, welfare benefits, competitiveness and protections for countries outside the eurozone.

A deal would kick off vigorous campaigns both for and against EU membership for Britain, which has been ambivalent about the bloc since almost the moment it joined. If there is a deal, Mr. Cameron will launch an intense campaign to keep Britain in the EU, while euroskeptics will intensify their efforts to persuade Britons to vote to leave.

Despite differences among European leaders at the summit, including over how long Britain could restrict social-welfare benefit payments to EU migrant, most still expect a deal to be secured.

After the first day of the two-day meeting ended, European Council President Donald Tusk, the point person for the bloc’s negotiations with the U.K., said, “We have made some progress but a lot still remains to be done.”

German Chancellor Angela Merkel said there remained more work to do in coming hours—for example to make sure there remained a level playing field for financial markets inside and outside the eurozone. But she said all leaders wanted the U.K. to stay in the EU.

On his way into the meeting, Mr. Cameron said he expected “hard negotiations” over his government’s demands to restrict benefit payments to EU nationals in the U.K. and win greater safeguards for the minority of EU countries who remain outside the eurozone.

“If we can get a good deal, I’ll take that deal, but I will not take a deal that doesn’t meet what we need,” Mr. Cameron said.

The key concession the EU offered to the U.K. in a set of proposals made Feb. 2 was the application of a so-called emergency brake, which would allow London to restrict tax credits for four years for future EU workers who come to the U.K.

Mr. Cameron argues the measure would discourage EU workers from coming to Britain and has made the concession central to his argument that he has won significant reforms from the EU.

Mr. Tusk, the point person for the bloc’s negotiations with the U.K., had deliberately left open how long the brake could remain in place, saying only there should be an initial period with the possibility of extending the measure twice.

On Thursday evening, Mr. Cameron was pushing for a total period of 13 years for the brake, according to several people familiar with discussions. The prime minister wanted an initial seven-year period for the brake, with the option for two extensions of three years’ each.

Other countries were pushing for a much shorter period. Some East European governments wanted the brake to apply for a maximum of only five years, according to three people familiar with conversations. A German government official said on Wednesday a seven-year maximum was a good basis for discussion.

The U.K. faces a fight over other issues too, including its push for safeguards for the minority of EU countries not in the eurozone.