Mr Varadkar is also due to meet EU Chief Brexit negotiator Michel Barnier, the European Parliament's representative in the Brexit negotiations Guy Verhofstadt, European Council President Donald Tusk and the European Commissioner for Agriculture and Rural Development, Phil Hogan.
With less than two months before Britain is scheduled to leave the EU, Tusk, who has an Irish speechwriter, said the priority is now to prevent a no-deal Brexit.
While many people in Britain and across Europe hoped that Britain might stay - something Tusk has repeatedly said was possible - he said he had concluded that there was now "no political force and no effective leadership" for those wanting to remain in the European Union.
As the men shook hands, Varadkar told Tusk "they will give you awful trouble in the British press" over the comments - which, as predicted, drew outrage from British Brexiteers. At the moment, the pro-Brexit stance of the United Kingdom prime minister, and the Leader of the Opposition, rules out this question.
He was speaking after talks with Irish premier Leo Varadkar in Brussels.
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In the news conference, Tusk said he was trying to forge ahead with the British but also warned that European leaders were preparing for the "possible fiasco" of a no-deal Brexit. "We will not gamble with peace; or put a sell-by date on reconciliation", Tusk said in a statement.
Donald Tusk today blamed Jeremy Corbyn's 'pro-Brexit' stance for killing off hopes of keeping Britain in the EU.
The prime minister's official spokesman said: "We had a robust and lively referendum campaign in this country".
The Northern Irish Democratic Unionist Party (DUP), which has propped up May's government since she lost her parliamentary majority in a 2017 snap election, said it wanted to get a deal agreed but the border backstop had to be replaced. Tusk's appearance alongside Varadkar was the latest signal that the bloc will not abandon Ireland, which fears both the economic and political impact of a hard border.
He said other European Union members had offered "unwavering commitment to protecting hard won peace and stability".
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Les deux clubs s'étaient entendus sur un versement en trois fois, comme cela est relativement courant dans les grosses transactions.
"What Parliament has said is that they believe there should be changes made to the backstop".
The Irish prime minister again insisted that there were no "alternative arrangements" to the already agreed Northern Ireland backstop.
Critics of the backstop argue its lack of any agreed time-limit is unacceptable as it could see the United Kingdom locked into a customs union deal with the EU indefinitely and Northern Ireland kept under EU single market rules.
May, on a visit to Belfast on Tuesday, tried to reassure Northern Ireland that she can deliver an orderly Brexit that will ensure peace in a province riven by three decades of sectarian conflict until a 1998 accord.
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