But The Guardian says the PM "irritated" the leaders by offering no new ideas to solve the Irish border question, instead highlighting the progress made by officials since the Salzburg summit last month.
The backstop is a proposed mechanism to keep the United Kingdom in the EU's Customs Union after Brexit - essentially precluding the country from taking back control of its global trade policy - in order to prevent a hard economic border between the British province of Northern Ireland and EU member the Republic of Ireland.
Speaking to the BBC on Thursday, the prime minister said she hoped that no extension would be needed but acknowledged that it may be necessary to lengthen the transition period by a "matter of months".
An extension of the UK's Brexit transition period "probably will happen", the President of the European Commission has said, in a move that will further anger Tory MPs, and isolate Theresa May.
"But the point is this is not expected to be used because we are working to ensure that we have that future relationship in place by the end of December 2020".
But, after Britain's refusal to accept an indefinite legal "backstop" to prevent the return of a hard border between Northern Ireland and the Irish Republic, doubts are mounting.
But even an extension will not get rid of the EU's insistence that such a backstop must be agreed to secure a deal.
U.K. Prime Minister Theresa May said she is weighing a plan that would keep the U.K. bound to European rules for longer, in an attempt to break the deadlock in talks.
After Brexit talks broke down last weekend, French President Emmanuel Macron said on Monday, "I believe in our collective intelligence, so I think we can make progress". "The tone was of someone who wants to reach an agreement".
With the talks stalled and little prospect of a quickening of pace, many Brexit supporters and critics of Britain's departure are airing their frustration over an exit which some campaigners had said would be an easy deal. May has offered to keep the whole of the United Kingdom in a customs union temporarily.
Instead, the matter could either be pushed back to December or - more dramatically - the European Union could use the November weekend to meet on preparations for a "no-deal" Brexit.
Rise in hate crimes with 52 % of religious offences against Muslims
Hate crimes against gay and bisexual people in the United Kingdom have rocketed by double-digit figures , new statistics show. New measures include taxi drivers and door staff being given guidance on spotting hate crime under a new Government clampdown.
"I'm clear that it is possible to do that and that is what we are working for".
"I want to see what the outcome is and the detail", they told BI.
On Thursday afternoon, European Union leaders, Switzerland and Norway were due to meet with 21 Asian leaders including Chinese Prime Minister Li Keqiang, to promote ties between the two regions.
Of course, given the gravity of the ongoing Brexit talks, there were some unsurprising interruptions from fellow bar-goers, inquiring as to how negotiations were going.
"The only answer to public disillusionment with how Brexit has not lived up to what they voted for is a People's Vote on the final Brexit deal".
A Conservative Eurosceptic has warned extending the Brexit transition period could cost the British taxpayer a "stratospheric" amount of money.
The European Union's top trade official is playing down the importance of a USA announcement that it will pursue a trade deal with Britain, noting London can not negotiate such pacts until it leaves the bloc.
"Today, we do not know what they want", she said.
May urged both parties to show "courage, trust and leadership", but came to Brussels without the concrete new proposals the European Union has asked for.
Mrs O'Neill said: "In order to preserve her toxic alliance with the DUP, she is trampling over the rights of citizens by acquiescing to that party's refusal to share power (at Stormont) on the basis of equality".