Update 12.40pm The President of the European Commission says he would be willing to add wording to the Political Declaration on the future relationship between the EU and UK post Brexit.
However Jean Claude Juncker told the British Prime Minister Theresa May in talks today that the Withdrawal Agreement will not be reopened.
The discussions in Brussels were described as robust but constructive.
The two leaders have agreed that their teams should hold talks to see if a way through can be found, and they will meet again before the end of February to evaluate these discussions.
Earlier: May arrives in Brussels for Brexit talks after backstop warning
Theresa May has arrived in Brussels for crunch Brexit talks after insisting that the UK must not be “trapped” in a backstop deal.
The British Prime Minister is meeting EU leaders on Thursday in the wake of the latest war of words between the two sides.
The spat was triggered by European Council president Donald Tusk saying there was a “special place in hell” for those who pushed for Brexit without a plan.|
The PM was greeted by European Commission president Jean-Claude Juncker at EU headquarters.
Both leaders struck a business-like stance as they posed for pictures, but did not answer questions.
One reporter asked: “Is this hell Prime Minister?”
David Lidington, who is effectively Mrs May’s deputy, said Mr Tusk’s comment “wasn’t the most brilliant diplomacy in the world”.
He told BBC Radio 4’s Today programme: “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.”
Mrs May’s latest diplomatic offensive comes as Labour leader Jeremy Corbyn wrote to the PM setting out five demands, including joining a customs union, that would need to be met for Labour to back the Government on Brexit.
The PM is using the top level Brussels talks with Mr Juncker, Mr Tusk and other prominent EU figures to press for legally binding guarantees on the Northern Ireland backstop.
At present the backstop, which is intended to prevent the return of a hard border in Ireland, would see the UK continue to obey EU customs rules after a transition period if no wider trade deal had been reached.
Downing Street said that Mrs May is “open to different ways” of achieving her objectives on the backstop.
The PM is using the meetings to state that Parliament has sent “an unequivocal message that change is required”.
One of the PM’s key messages for EU leaders is that the Commons has made it clear it could support the Withdrawal Agreement as long as concerns about the backstop are addressed.
Mrs May is also stressing that Mr Corbyn also has concerns about the backstop, so it is not just an issue for the Tories and their DUP allies.
In Mr Corbyn’s letter to the PM, which follows their Brexit meeting last week, he insists that Labour’s Brexit demands must be enshrined in the Political Declaration setting out future relations with the EU.
Mr Corbyn said that securing in law the demands is the only way of achieving Labour support and uniting the country.
He calls for a “permanent and comprehensive UK-wide customs union” that gives the UK a say over future trade deals, and close alignment with the single market, underpinned by “shared institutions”.
Mr Corbyn also calls for “dynamic alignment on rights and protections” in order that UK standards do not fall behind those of the EU, as well as commitments on participation in EU agencies and funding programmes, and “unambiguous agreements on the detail of future security arrangements, including access to the European Arrest Warrant and vital shared databases”.
The letter drew criticism from some pro-EU Labour figures who said it went against Labour’s Brexit stance.
Among the prominent EU figures Mrs May is meeting is European Parliament Brexit coordinator Guy Verhofstadt who joined in with Mr Tusk’s Brexit “hell” analogy.
Mr Verhofstadt tweeted that Lucifer would not welcome such Brexiteers because “after what they did to Britain they would even manage to divide Hell”.
Meanwhile, the Daily Telegraph reported that Mrs May is seeking to delay another Commons “meaningful vote” on the Government’s Brexit stance until the end of February – just a month before the UK is Government’s Brexit stance until the end of February – just a month before the UK is scheduled to quit the EU on March 29.