Summit will carry on until Friday, but the Brexit issue is Wednesday's agenda. "We need a bigger vision that people can coalesce around", he said. He added the Irish border problem is "more hard to solve than Gibraltar".
Rutte said that while it "would be great if we succeed this week", negotiators will take more time if the summit doesn't produce an agreement.
The three-hour session saw discussions on the Northern Irish border backstop, where Downing Street said ministers voiced "shared concerns".
The official also said May had been invited to attend a bilateral meeting with summit host Donald Tusk, the president of the European Council, before her speech to the leaders.
The Cabinet will meet on Tuesday morning to discuss the state of Brexit negotiations before May travels to Brussels on Wednesday evening.
The prime minister told a cabinet meeting on Tuesday morning she could not agree to any deal with the EU which created a new border between Northern Ireland and the rest of the United Kingdom - or one which locked the United Kingdom into a customs union with the EU indefinitely.
The key sticking point is the backstop. May can do nothing else but hope for a breakthrough.
DUP leader Arlene Foster was in Dublin yesterday for meetings with the Taoiseach Leo Varadkar and others.
Britain refuses to be pinned down on a date for a fixed Brexit deal.
Her most recent European Union summit experience was a bruising one, with Tusk and others rejecting her proposals and blasting the UK's attitude towards negotiations. This may not go as well as she hopes: Labour would be deeply foolish to tie themselves to a compromise deal which will be detested by Remain and Leave voters alike.
Northern Ireland's Democratic Unionist Party, which British Prime Minister Theresa May's government depends on for support, believes a no-deal Brexit is "probably inevitable", the party's Brexit spokesman was quoted as saying on Monday.
May has insisted that she would never agree to the EU's proposal, which would separate Northern Ireland constitutionally and economically from the rest of the UK.
"And they want this to be the Northern Ireland-only solution that they had previously proposed".
The prospect of a no-deal exit from the European Union is an equally major threat that looms over the Theresa May led government.
Donald Tusk has poured cold water on hopes of a Brexit breakthrough at Wednesday's European Union summit, saying the Irish border was still a sticking point.
"The problem is at the British end", a diplomat said.
"The right message is to say: "a deal is possible, but we are in a hurry and we should finalise a withdrawal agreement with a backstop quickly".
Both sides say much of the withdrawal agreement, which sets the divorce terms for Britain's departure, has been agreed, but there are still outstanding issues, mostly on the backstop. "That's new. It hasn't been there before".
Also it is confirmation, if such were needed, of how hard it is for Barnier to drop a solution for Northern Ireland that introduces trade barriers with Great Britain.
May updated MPs as she prepares to secure a Brexit divorce deal with the EU.
The EU's chief negotiator told ministers from the 27 member states that he is prepared to work on fresh ideas even at this late stage.
"I think we all would like to see this concluded as soon as possible".
"Whether we do (it) this week or not, who knows?" I felt it will take until November to get done.
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