The Irish and German leaders have discussed how to help Theresa May get her Brexit deal through Parliament.
Taoiseach (Irish PM) Leo Varadkar said he held a 40-minute phone call with German Chancellor Angela Merkel on Thursday morning at her request.
He said they agreed to offer reassurances and guarantees to the UK, but would not change the existing deal.
Meanwhile, DUP deputy leader Nigel Dodds reiterated objections to the deal during a meeting with Mrs May.
His party, which is propping up Mrs May's government, is strongly opposed to the Irish border backstop element of the draft EU withdrawal agreement and described concerns over a hard border as "nonsense propaganda".
The draft deal requires the support of Parliament, and the prime minister is facing significant opposition from a cross-section of Westminster MPs, including the DUP.
Addressing reporters in Dublin on Thursday afternoon, Mr Varadkar said Brexit "was a problem created in the UK" and it was up to Westminster to offer a solution.
"It was an opportunity to brain storm a bit as to what we could do to assist Prime Minister May in securing ratification of the withdrawal agreement," Mr Varadkar said of his conversation with Mrs Merkel.
Planning for a no-deal Brexit was also discussed during their phone call.
"What we both really agreed was that, once again, this is a problem that's created in London," Mr Varadkar said.
"The inability to ratify the withdrawal agreement is a problem in Westminster, and we're really looking to them for a solution," he said.
"But it has to be a proposal that we can accept. So it can't be a proposal that contradicts what is already in the withdrawal agreement.
"It can't be something that renders the backstop inoperable, for example. So we want to be in a position to give guarantees, give assurances, give clarifications."
The taoiseach added that the Irish border was the only "red line" his country has had in the Brexit negotiations and that would not change.
The DUP criticised the Irish government's strategy after several of its senior figures had lunch with Mrs May on Thursday.
"The Irish Republic's 'no deal' preparations published just before Christmas have laid bare the nonsense propaganda about a hard border," Mr Dodds said.
"No one wants a hard border between Northern Ireland and the Republic. Indeed, its becoming clearer by the day that no one is ever going to construct such a border.
"With this clarity emerging in London, Dublin and Brussels, there is evidently no need for the aspects of the Withdrawal Agreement which have been so vigorously opposed by a broad cross section of the House of Commons."
Mr Dodds repeated his party's claim that the backstop would place a "barrier" between Northern Ireland and its "main trading partner", Great Britain.
"Brussels must now demonstrate that if it truly cares about Northern Ireland, then erecting a new east-west barrier should be no more palatable than having any new north-south barriers," he said.