Theresa May and Jean-Claude Juncker have described their talks on changing the Brexit deal as « robust but constructive », in a joint statement.
The European Commission President stressed the withdrawal agreement could not be changed, as the UK PM wants.
But he said the EU was open to adding words to the non-binding future relations document that goes with it.
The two leaders agreed to meet for further talks before the end of February.
The EU and UK Brexit negotiating teams are, meanwhile, set to resume their talks.
Mrs May is insisting the UK will not be « trapped » in the backstop – the plan to avoid the return of Irish border checks whatever UK-EU trade deal is agreed.
She says the plan must change if it is to win the support of MPs who urged her to seek « alternative arrangements » when rejecting the deal last month.
Mrs May’s visit comes after the row over Wednesday’s outburst by Donald Tusk, who declared there was a « special place in hell » for those who campaigned for Brexit without a plan to deliver it safely.
MPs who backed Leave in the 2016 referendum reacted with anger to the comments, accusing the European Council president of « arrogance ».
David Lidington, the minister seen as Mrs May’s second-in-command, said Mr Tusk’s comment « wasn’t the most brilliant diplomacy in the world ».
Mr Lidington told BBC Radio 4’s Today: « I think Mr Tusk was venting yesterday, but I don’t think that will detract from what I expect to be a courteous and sensible grown-up discussion between the different EU leaders and the prime minister. »
Labour’s fresh offer to May
Jeremy Corbyn has written to the prime minister setting out his party’s price for supporting a Brexit deal and to offer talks to secure « a sensible agreement that can win the support of Parliament and bring the country together ».
The Labour leader’s five demands include a « permanent and comprehensive UK-wide customs union » aligned with the EU’s customs rules but with an agreement « that includes a UK say on future EU trade deals ».
Mr Corbyn also wants close alignment with the EU single market and « dynamic alignment on rights and protections » for workers so that UK standards do not fall behind those of the EU.
He also proposes participation in EU agencies and funding programmes, and agreements on security and keeping access to the European Arrest Warrant.
The letter does not mention previous demands that any deal must deliver the « exact same benefits » that membership of the single market and customs union currently does – effectively scrapping the party’s « six tests » that had been its Brexit policy.
The BBC’s Political Editor Laura Kuenssberg said Labour’s shadow Brexit secretary Sir Keir Starmer would be meeting cabinet office minister David Lidington to discuss the proposals.
But the move was met with dismay by Labour members of the People’s Vote campaign for another EU referendum, who accused Mr Corbyn of going back on his commitment, made at the party’s conference, to back a public vote if he can’t force a general election.
Labour MP Chris Leslie tweeted: « Seriously? Offering to help Tory Govt enable Brexit? It’s not just Labour’s conference policy in the bin.
« When the jobs go & revenues for services dry up as a result – Labour’s leadership will have ZERO right to complain: they share responsibility. »
Mr Lidington said he and Brexit Secretary Steve Barclay would be willing to discuss Labour’s proposals with Sir Keir and other frontbenchers.
But he said Labour’s call to have a say in trade deals while being in a customs union with the EU was « wishful thinking », because Brussels had ruled it out.
Analysis: What awaits Theresa May in Brussels?
By BBC Europe editor, Katya Adler
There’s pretty much zero expectation that any real progress will be made on Thursday when Theresa May comes back to Brussels looking for changes to the backstop.
Mr Tusk is not alone in Europe in his frustration at leading Brexiteers’ unrealistic promises…
EU leaders are irritated too that – as they see it – the UK voted for Brexit but keeps looking to Brussels to come up with ways to make its exit workable and painless.
But most senior European politicians are keeping those thoughts quiet – in public.
Considering the tortuous political dance Theresa May is trying to pull off in Westminster, they realise outspokenly critical EU opinions may not be helpful if, in the end, they want to get this Brexit deal done with the UK.
- Read Katya’s analysis in full
Where are we in the Brexit process?
The UK is due to leave the EU at 23:00 GMT on Friday 29 March, when the two-year time limit on withdrawal negotiations enforced by the Article 50 process expires.
In January, MPs overwhelmingly rejected the withdrawal deal that the government had negotiated with the EU, backing an amendment for the government to seek « alternative arrangements » to the backstop.
The backstop is an « insurance policy » designed to avoid « under all circumstances » the return of customs checkpoints between Northern Ireland and the Irish Republic after Brexit.
Many fear creating physical infrastructure along the border could threaten the peace process.
But the Democratic Unionist Party and Brexiteers believe the proposed temporary single customs arrangement could threaten the integrity of the UK, leaving it bound by EU rules if no trade deal is agreed.
Mrs May is due to meet European Commission president Jean-Claude Juncker, European Council president Donald Tusk and other senior figures on Thursday.
Downing Street said one of the Mrs May’s key messages will be that the Commons has now made it clear it could support the withdrawal agreement, as long as concerns about the backstop are addressed.
‘A trusted friend’
The prime minister will use the meetings to state that Parliament has sent « an unequivocal message that change is required ».
Mrs May is « open to different ways » of achieving her objectives on the backstop, Downing Street said.
She will also stress that Mr Corbyn shares the concerns about the backstop, saying that it is not just an issue for the Conservatives and the government’s DUP allies.
Both sides must « show determination » to get an exit deal « over the line », Mrs May will say.
Downing Street said the government wanted to bring back a « meaningful vote » on a Brexit deal to the Commons as soon as possible.
On Wednesday, Mr Tusk said the Irish border issue and the need to preserve the peace process remained the EU’s top priority.
He hoped Mrs May would « give us a deliverable guarantee for peace in Northern Ireland and the UK will leave the EU as a trusted friend » that can command a Commons majority.
Taoiseach (Irish prime minister) Leo Varadkar said that while he was « open to further discussions » with the UK government about post-Brexit relations, the legally-binding withdrawal agreement remained « the best deal possible ».
And the backstop was needed « as a legal guarantee to ensure that there is no return to a hard border on the island of Ireland ».
He is due to meet Mrs May for talks in Dublin on Friday.