LONDON — Prime Minister David Cameron claimed ‘‘real progress’’ Tuesday in negotiations with the European Union, but said more work needs to be done before a satisfactory agreement on reform of the bloc can be approved at a summit this month.

Cameron told sometimes skeptical British voters that he is close to achieving a deal that would satisfy many of his demands for a fundamental change in Britain’s relations with the European Union.

He spoke after European Council president Donald Tusk unveiled proposals aimed at keeping Britain in the 28-nation EU.

The proposals would make it possible for British lawmakers to work with European counterparts to block unwanted EU laws and also recognize that Britain now faces an ‘‘exceptional situation’’ regarding the influx of immigrants taxing Britain’s social services.

They would end Britain’s commitment to an ‘‘ever closer union’’ with Europe and recognize its ability to stay out of the euro single currency.

Cameron is seeking concessions ahead of a planned referendum on whether Britain should remain part of the EU. That vote may be held as early as June. He said the document delivers the ‘‘substantial change’’ he had sought.

‘‘On so many things, I was told these things would be impossible,’’ he said. ‘‘I said I wanted a red card system for national parliaments to block legislation. People said you wouldn’t get that. It’s there in the document.’’

He also cited progress in his concerted bid to make citizens of other EU nations wait before claiming welfare benefits in Britain.

The draft deal was made public in a letter to EU leaders. It must be endorsed by Britain’s EU partners and is set to be finalized at a summit in Brussels on Feb. 18.

It is not clear whether the proposal as it now stands will placate many Britons who have come to resent the EU’s rule-making power and worry about the arrival on European shores of more than 1 million people fleeing war and poverty in the past year.

Nigel Farage, leader of the UK Independence Party and an outspoken advocate of taking Britain out of the union to ­restore full sovereignty, called the draft proposal ‘‘truly pathetic’’ since it does not change EU treaties and does not restore Britain’s ability to control its borders and its laws. He said it does too little to limit welfare payments to migrants and does nothing to close Britain’s ‘‘open door’’ to new arrivals.

‘‘There is no fundamental reform, there’s some fiddling around the edges on migrant benefits,’’ he said.

Some business leaders struck a more positive note. ­Simon Walker, director general of the Institute of Directors, said the deal is better than had been expected.

‘‘The top reform priorities for [Institute of Directors] members are to stop the flow of unnecessary red tape from Brussels, make clear the UK is not on a path to more political integration, and make the EU more competitive,’’ he said. ‘‘There are proposals on these areas in Tusk’s draft which hold promise, although no one should get carried away just yet.’’

He cautioned that most of the group’s members are waiting to see the final outcome of negotiations before deciding whether to give thumbs up or down to continued EU membership.

Tusk said in his introduction to the proposals that he addressed Cameron’s concerns but did not agree to any alterations to ‘‘the principles on which the European project is founded.’’

He said maintaining the EU’s unity is the key challenge for the bloc. It has been tested by the unprecedented migrant influx, several financial crises, and Britain’s growing disenchantment. More compromise is needed or the bloc will fail, Tusk said.

On the contentious issue of benefits for EU migrant workers, Tusk says that EU treaties must be respected, but he suggests there is room for maneuver by saying that current rules on the free movement of people could be clarified.

The EU’s executive Commission has drawn up a ‘‘safeguard mechanism’’ that could be used for Britain to respond to ‘‘exceptional situations of inflow of workers’’ from other EU countries.

The plan aims to meet the concerns of Britain about its membership terms and perceived loss of sovereignty to Brussels without requiring time-consuming changes to the EU’s legal treaties.