By Elizabeth Piper and Gabriela Baczynska
BRUSSELS (Reuters) - Prime Minister Theresa May and other EU leaders voiced renewed confidence on Thursday they could secure a Brexit deal, saying they were working hard to overcome the hurdles that only days ago brought the talks to a halt.
Less than six months before Britain quits the EU in its biggest shift in policy for more than 40 years, the two sides are at odds over how to deal with their only land border, between the British province of Northern Ireland and Ireland.
But while the mood at a two-day summit in Brussels was more upbeat, there was little movement from either side on how to resolve the border issue, with EU officials and diplomats saying May had offered nothing new to unlock the talks.
For now, however, both sides seemed to be happy to kick any solution to that problem a little bit further down the road.
"We are all working, we're intensifying the work on these issues that remain," May told a news conference after a two-day summit in Brussels had ended.
"What I've had from leaders around the table ... since I arrived here in Brussels yesterday is a very real sense that people want that deal to be done."
"I am confident that we can achieve that good deal."
It was a marked change of tone since May's Brexit minister Dominic Raab left Brussels on Sunday after the more than year-long Brexit talks broke down over the border issue.
The problem centres on a so-called backstop - an insurance policy to ensure there will be no return to a hard border on the island of Ireland, a former focal point for sectarian tensions, if a future trading relationship is not in place in time.
To try to move the talks forward, May had earlier signalled she would consider extending a so-called transition period "for a matter of months" after Britain leaves the EU in March, a move her critics called a betrayal but one which the bloc welcomed.
Extending the transition period could mean that if a future partnership is not ready, a backstop, which so far has been unpalatable to the British side, would not have to be triggered. But even an extension would not get rid of the EU's insistence that such a backstop must be agreed to secure a deal.
TRANSITION
Such an extension would be difficult for May to sell at home, where her overall strategy has been criticised by all sides -- Brexit campaigners accuse her of making Britain a vassal state, EU supporters say the offer is the worst of all worlds and others are increasingly frustrated over the talks.
One prominent Brexit supporter, Conservative lawmaker Jacob Rees-Mogg, told Reuters that any extension to the transition was "a bad and expensive idea". "No say on the budget or new laws, the epitome of the vassal state."
May also faces a rebellion from her parliamentary partners, Northern Ireland's Democratic Unionist Party, which has threatened to vote against her government's budget if she concedes to the EU's demands over the backstop. They say the proposal would tear Northern Ireland from the rest of Britain.
Diane Dodds, an EU lawmaker from the DUP, said the extension did not ease her party's fears. "All very well, but this doesn't do anything to actually change the backstop ... Therefore it does not address any concerns, it offers no reassurance."
With the EU showing little sign of changing its position on the backstop, its leaders could offer May little more than the support that they too believed a deal could be reached. Diplomats say they hope talks could re-start in earnest when, and if, the budget gets passed in early November.
EU Council President Donald Tusk described the mood as much better than the one at the last summit in Salzburg, which ended in acrimony. "What I feel today is that we are closer to the final solutions and the deal," he told a news conference.
Jean-Claude Juncker, EU Commission president, said: "It will be done."
But the Northern Irish question still has to be overcome. May expressed hope that it could be all but negotiated away by the two sides agreeing a close future partnership, which would ensure borders that are as frictionless as possible.
The EU's leaders were more circumspect.
Irish Prime Minister Leo Varadkar summed it up by saying "big gaps" remained between the two sides "both in terms of the shape of the future relationship and also the protocol on Northern Ireland and Ireland and the backstop".