The two sides are at a "critical point" in these negotiations, a spokeswoman for May said
EU chief negotiator Michel Barnier and his British counterparts on Tuesday wrapped up the latest round of talks aimed at getting the Brexit deal through parliament in London as this month's divorce deadline loomed.
Barnier met UK attorney general Geoffrey Cox and Brexit minister Stephen Barclay for four hours over dinner, an EU official told AFP following conciliatory signals from both sides.
The official could not confirm whether the talks would resume on Wednesday when he said journalists would be briefed on the results of Tuesday's meeting.
Barnier said Saturday the European Union was ready to give further guarantees to help the Brexit deal it struck with Prime Minister Theresa May in November get through the British parliament.
Barnier also suggested European leaders would be amenable to a short "technical" delay in Britain's departure from the bloc scheduled for March 29, to give parliament time to formally ratify a final accord.
"We are determined to get a deal over the line and deliver on Brexit," Barclay tweeted as he and Cox, the government's top lawyer, departed for Brussels.
There was no immediate comment from Barclay after the talks ended.
Barnier's small overture to Britain has raised some hopes that both sides can find a solution, including to the so-called "backstop" plan for the Irish border, a major sticking point for pro-Brexit MPs.
The two sides are at a "critical point" in these negotiations, a spokeswoman for May said earlier on Tuesday.
Cox's presence is seen as central as he will ultimately offer a legal opinion on the Brexit deal and the Irish backstop that could determine whether key pro-Brexit lawmakers will approve the withdrawal agreement.
The EU sees the backstop as an insurance policy to keep open the border between EU member Ireland and British Northern Ireland -- and to preserve the island's peace process.
'Prepared to be flexible'
Earlier advice by Cox, warning that the backstop could keep Britain tied permanently to an EU customs union, was viewed as a contributing factor in the massive defeat of May's deal by MPs in January.
EU leaders insist the legally binding withdrawal agreement will not be reopened, and the talks in Brussels are focused on drafting a separate document to placate doubters in London.
Also raising hopes are the softening positions of several hardline Brexit supporters in May's Conservative party who have dropped their demand that changes to the backstop be made in the withdrawal treaty itself.
But most of them continue to press for a time limit or exit clause to the backstop. They have also set up their own team of lawyers to scrutinise anything that Cox brings back from Brussels.
British foreign minister Jeremy Hunt told BBC radio on Tuesday his government is getting "reasonably positive" signals from officials in EU capitals who he says are starting to realise the deal can get through parliament.
Hunt said avoiding an indefinite backstop was the crucial issue, when asked whether London was sticking to either a time limit or a unilateral exit mechanism from the backstop.
He added: "How we get there is something we are prepared to be flexible about".
Eurasia Group analyst Mujtaba Rahman, a former UK official, said "many Tories who dislike May's deal are reluctantly coming round to the idea of voting for it."
Cox will likely "reverse his previous legal advice that the UK could be trapped 'indefinitely' in the backstop," Rahman predicted.
In 2017, Britain invoked Article 50 of EU law, triggering a two-year countdown to Brexit that ends at 11:00 pm (2300 GMT) on March 29.
Both sides are furiously trying to steer away from a dreaded "no-deal" divorce that could wreak havoc on global markets and create border chaos.
With fears about financial and economic stability growing, British lawmakers last week agreed to give May more time to seek changes from Brussels, but if she cannot get her deal passed by March 12, she has agreed to let parliament vote for a Brexit delay.