"I am hoping that in Salzburg we will be able to put an end to the mutual resentment and return to a constructive approach", he wrote in a summit invitation letter.
British Prime Minister Theresa May told rebels in her divided party that if they torpedoed her Brexit deal then the United Kingdom would leave the European Union without any agreement, a scenario the International Monetary Fund said would make the country much poorer.
European Union council president Donald Tusk, in his invitation letter for a meeting of European Union leaders In Salzburg on Thursday, said he would raise the issue of organising another summit.
Both the EU and the United Kingdom said they wanted to avoid a hard border between the Republic of Ireland and Northern Ireland, as it becomes the union's external border after Brexit in order not to risk the fragile peace agreement achieved on the island in 1998.
"I want to ensure that as we go forward we have that strong union..." PM Theresa May explains what the government has agreed, and what this means for us leaving the EU.
Mrs May's short address over dinner is not expected to be followed by a full discussion, with the EU27 leaders due to talk about the way ahead for Brexit in her absence on Thursday.
The Irish border issue is the biggest barrier to reaching such an agreement, the committee said.
The EU's backstop proposal has been rejected by the UK because it effectively creates a customs border in the Irish sea, while the UK's plan was rejected by the UK because it was temporary and applied to the whole of the UK, rather than only Northern Ireland.
"We have to do everything possible to avoid a hard Brexit and to make possible that there will be a strong cooperation between the United Kingdom and the European Union", Kurz said Monday ahead of talks with French President Emmanuel Macron.
Mr Varadkar told the Dail parliament in Dublin: "I do not anticipate there will be any change to the EU's position or any change to our negotiating guidelines".
The former foreign secretary's warning came as Mrs May gave one of her most positive forecasts yet for Britain's future after Brexit, telling the BBC: "I believe that our best days are ahead of us".
A demonstration at the Labour conference in Liverpool on Sunday will add to pressure on Jeremy Corbyn to throw his weight behind calls for a second referendum.
Third, Tusk said, the leaders should "reconfirm the need for a legally operational backstop on Ireland, so as to be sure that there will be no hard border in the future".
Tusk, who last weekend held talks in Cairo with general-turned-president Abdel-Fattah el-Sissi, urged the leaders to consider co-operation on migration with Egypt, saying that "it is worth recalling that the Egyptian authorities have made the fight against smuggling and trafficking their priority".
"Unfortunately, a no-deal scenario is still quite possible". With goodwill and determination on both sides, we can avoid a disorderly exit that would cause us all great difficulties and find new ways of working together.
Commissioned by the government and published on Tuesday, the report concluded that free movement from the European Union should end after Brexit.
The long-awaited study also concluded that the post-Brexit immigration system should make it easier for higher-skilled workers to come to the country.
At the same time, he stressed that any backstop would "fully respect the territorial integrity of the UK" and "only apply unless and until a better solution is found, in the context of our future relationship".