Mr Barnier said: "My line is to work for an orderly withdrawal of the United Kingdom, including an operational solution for Ireland and Northern Ireland; that is my line".
The EU will consider "any solution" on Brexit which would allow it to maintain the integrity of the Belfast Agreement, the EU's chief Brexit negotiator Michel Barnier has said during a visit to Derry.
Mr Barnier called for new proposals from the British to avoid a hard border on the island of Ireland and warned that unless there was a new proposal beyond the so-called backstop option to keep Northern Ireland under European Union economic rules, there was a danger that negotiation could collapse.
Mr Varadkar said he was resolutely committed to protecting the peace process across Ireland.
"I think he's minded to come up with a solution that works best for the unique scenario that we have in this region".
She said: "During his visit Michel Barnier heard the concerns of local stakeholders about the impact of Brexit and the prospect of the imposition of a hard border and the need for the north to secure special status within the EU".
It was left to the third MEP, Sinn Féin's Martina Anderson, to greet Barnier when he arrived at the Guildhall on Tuesday.
"We have to acknowledge that the continued absence of functioning political institutions in Northern Ireland is, at least partly, a outcome of concerns about, and different positions on, Brexit".
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"I also made it clear to Michel Barnier in our meeting that the DUP do not speak for the people of the north, a majority of whom voted to remain in the EU".
"We're as positive as we can be in, I suppose, what's an overall negative situation". The parliament is not open today. "On the other hand for Mr Barnier's visit to Dungannon the Council has not even been told that it is to happen", she said.
"I think it's political bad manners that the MEPs were both invited here this morning, and neither of them have turned up".
Anderson said: "All three of us should be maximising the opportunity when Michel Barnier is in our constituency".
"I don't think really when you have a chief negotiator coming from the European Union that it's a good signal to send out because I don't think it's representative of the people, the protestant, unionist, loyalist people, who would want their own representatives taking the opportunity to express their views", she said.
Negotiations have become bogged down over how to avoid a hard border on the island of Ireland.
Mr Varadkar acknowledged some unionists were anxious that Brexit could be used to undermine Northern Ireland's union with Britain.
She also said the DUP met him in Brussels "a few weeks ago" and insisted it was important to have "input" at the Brexit discussions in London.