On her last visit in November, she hailed the Withdrawal Agreement as a good deal for Northern Ireland and defended the controversial "backstop" as an essential safeguard in ensuring no return to a hard border with the Republic.
British Prime Minister Theresa May is due in Brussels on Thursday with what she says is a parliamentary mandate to re-open the draft agreement, sealed after 18 months of intense and highly technical negotiations.
But asked how she could convince the people of Northern Ireland to accept a Brexit deal which was stripped of the backstop, Mrs May said: "I'm not proposing to persuade people to accept a deal that doesn't contain that insurance policy for the future".
But speaking to an audience of business leaders and journalists on Tuesday, the PM said she wanted to "affirm my commitment to delivering a Brexit that ensures no return to a hard border between Northern Ireland and Ireland, which is unshakeable". Downing Street has previously suggested that these might revolve around a time-limit or unilateral brake on the backstop or technological solutions to keep traffic flowing over the border.
A press release on Tuesday said that Coveney would conduct other business besides Brexit while in the U.S. In New York on Tuesday, he will undertake engagements in support of Ireland's campaign for a non-permanent seat on the UN Security Council, the election for which will take place next year.
"The prime minister has come here empty-handed, with the same old rhetoric, with no plan, no credibility, frankly no honor", said Mary Lou McDonald, president of the Irish nationalist party Sinn Fein.
Mr Varadkar also said Ireland is increasingly prepared for a no-deal Brexit.
Britain is scheduled to leave the bloc on March 29, but no withdrawal agreement has been approved because Britain's Parliament has voted down May's plan.
He added: "Alternative arrangements, they will never replace the backstop".More news: Washington State Reports More Measles Cases
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"We can have those conversations, so we can use the remaining time to perhaps remove the obstacles that have so far stood in the way and find an agreement if everyone is willing".
At this critical juncture, Northern Ireland is represented only by the Democratic Unionist party, which is not representative of the people on Brexit - and so much more.
Britain is due to leave the European Union on March 29.
She says "one has to be creative, and we must listen to one another" but that an agreement on the Irish border is still possible.
As the party that negotiated the Good Friday agreement, which brought peace to Northern Ireland, the Labour Party has a solemn duty to be responsible in our approach to the effects of Brexit on Northern Ireland and the Good Friday agreement - no matter how great the desire to see a change in government, we can not forget our responsibility to the peace process and to protecting its integrity.
They voted to demand May seek changes to the treaty.
Mr Tusk added that the European Union was not making "any new offer" to the UK Government on the Brexit deal and he repeated the EU's insistence that the Withdrawal Agreement reached with Theresa May a year ago could not be reopened.
Visiting Brussels yesterday, Mr Varadkar was refusing to back down yesterday, however, saying he had had concerns about Mrs May's suggestions of "alternative arrangements" for the Irish border and saying the proposal could not mean the "deletion" of the backstop.
The group was holding three days of meetings with ministers and civil servants to investigate possible changes to the European Union divorce deal, which was rejected by Parliament last month.