David Cameron is travelling to Poland and Denmark as he tries to win support for his package of reforms aimed at keeping Britain in the EU.
A draft agreement was published this week and the prime minister is hoping a deal will be backed in two weeks.
Proposals to curb EU migrants' benefits are expected to dominate the talks in Warsaw - Poland has said it fears its citizens could face discrimination.
The agreement has been dismissed as meaningless by "Out" campaigners.
The draft proposals were published by European Council president Donald Tusk on Tuesday after months of negotiations between UK and EU officials and pave the way for Britain's EU referendum to take place as early as June.
An EU source close to the negotiations told the BBC the proposals had met initial resistance from many countries and Mr Cameron faced two weeks of "difficult" negotiations before a summit in Brussels on 18 and 19 February.
Among the potential sticking points, the source said, were Mr Cameron's proposals on changing the EU rules to make it easier for member states to band together to block EU laws - and plans to protect non-eurozone countries.
Other issues include the proposal for an "emergency brake" on in-work benefits.
BBC political correspondent Ben Wright said that issue was certain to dominate the talks in Warsaw.
But our correspondent said Mr Cameron should expect a supportive welcome in Denmark - a country historically sceptical about the EU and which has opt outs and concerns which are similar to Britain's.
In Brussels ambassadors and officials from the 28 member states will meet for the first time since the proposals were published to try to hammer out further compromises.
Mr Cameron held talks on Thursday at Downing Street with European Parliament President Martin Schulz, who said afterwards the negotiations were "not at the end of the process" but that he was "optimistic" of finding a compromise.
The PM earlier met Mr Tusk, Slovak PM Robert Fico, Greek PM Alexis Tsipras, Swedish PM Stefan Lofven and Belgian PM Charles Michel on the margins of the Syria donors' conference in London.
Countries on the EU's eastern flank, meanwhile, are to meet next week before providing a joint response to the reform package, Hungary's foreign minister said.
Mr Cameron is also under pressure at home from some members of his own cabinet, who have been prevented from speaking out in favour of a British EU exit.
Culture Secretary John Whittingdale refused to rule out campaigning to leave the EU, in an interview with The House magazine, saying he would look at the agreement the prime minister managed to secure.
Follow mhiztabolu on twitter