Arlene Foster held a "very constructive" meeting with the Taoiseach yesterday and said a Brexit deal is possible, as far greater obstacles were overcome to secure peace.
Leo Varakdar met leaders from the five main local parties in Belfast and later returned to Dublin where he hosted the Prime Minister for dinner, as efforts continued to find a breakthrough.
Following her meeting with the Taoiseach, Mrs Foster said the DUP wanted a deal which worked for "London, Dublin, Brussels and Belfast" and would win support in the House of Commons.
"If there is genuine political will, then a deal is possible. Northern Ireland should stand as a reminder to the Taoiseach of how we have overcome many greater obstacles in the past," she said.
Mr Varadkar said everybody wanted to avoid a no-deal and a hard border and "to continue to have a very close political and economic relationship between Britain and Ireland no matter want happens".
He said: "There is much more that unites us than divides us and time is running short, and we need to get to an agreement really as soon as possible, and I'll be working very hard and redoubling my efforts, along with government, to do that."
He insisted that while the backstop was not up for renegotiation, "we can talk about the joint political declaration and what changes might be made to that and what assurances may be given that would assist this agreement being ratified".
Asked about the controversial comment of European Council president Donald Tusk that there was a "special place in Hell" for Brexiteers without a plan, Mr Varadkar pointed to anti-EU political rhetoric.
"It was only a few months ago that people in the UK Government were comparing the European Union to communism and bear in mind President Tusk spent much of his life fighting to overthrow communism," he said.
"So I think there has been a lot of rhetoric coming from a lot of different quarters and I think the best thing to do is just to rise above it."
The DUP leader said it was important for Mr Varadkar to understand that unionist views on the backstop could not be ignored.
"The EU must respect that, for unionists, a new border east-west is no more acceptable than a new border north-south," she said. "The draft withdrawal agreement was unacceptable because it would cut Northern Ireland off from the rest of the UK and create a democratic deficit in Belfast.
"We will test any new draft withdrawal agreement against its impact on the Union and whether it respects the referendum result."
She declined to be drawn on whether alternative proposals to the backstop had been discussed during the meeting. The DUP leader said she wasn't enthusiastic about extending Article 50 if a Brexit deal wasn't reached by March 29.
"What we are focused on is trying to find a deal. That is where everybody should be focused, and not focused on extending the time further," she said.
"Because I think, as you know, here in Northern Ireland if you give more time often you don't get the outcome."
DUP deputy leader Nigel Dodds, who also attended the meeting, said he believed a Westminster majority for a Brexit deal could be found with his party's MPs and some Labour rebels voting with the Tories.
Speaking after her meeting with Mr Varadkar, Sinn Fein's vice president Michelle O'Neill said: "I think the Taoiseach has remained firm throughout the negotiation in recognising the need to protect Irish interests, in recognising the need to make sure that citizens in the North are never left behind.
"He restated that commitment to us today. At the end of the day, we will hold the Taoiseach's feet to the fire on the issue."
She added: "Any retreat from it would jeopardise Irish interests, the peace process and the Good Friday Agreement. With the exception of the unionist parties, there is political unanimity north and south on the need to protect the backstop."
Ulster Unionist leader Robin Swann said there must be "realism" in Dublin about unionists' backstop concerns.
"The dismissal of these concerns will inevitably have long-lasting consequences for relationships north and south of the border," he said.
"Equating opposition to the backstop as beckoning the return of violence is an extremely dangerous and foolhardy position for the Republic of Ireland's Government to take.
"It is providing justification in advance for those who may attempt to turn the clock back."
Alliance leader Naomi Long said her party had a positive meeting with the Taoiseach and said it was reassuring that he had reiterated his support for the backstop.
Last night's one-on-one between Mr Varadkar and Mrs May came at the request of the British Government at the end of a week when she has travelled to Belfast and Brussels.
Her team was warned in advance by Irish officials that while they were happy to host her, any Brexit discussions could only be interpreted as "talk".
They stressed Ireland negotiates its position through the European Union taskforce led by Michel Barnier.
Mr Varadkar said the meeting was an opportunity "to share our perspectives and for us to listen to each other".
"There is much more that unites us than divides us and time is running short," he said.
The Prime Minister is believed to have used the meeting to explain her desire for legally binding changes to the Brexit deal.
This has been repeatedly ruled out by Mr Varadkar and key EU leaders.
