The DUP had a "constructive dialogue" with Cabinet ministers over Brexit on Friday as the Prime Minister desperately seeks to build support for her deal after it suffered a fresh setback.
Backing from the DUP could lead to Mrs May’s deal being approved by the Commons next week, after it was defeated for the second time on Tuesday.
The talks come as European leaders consider whether to agree to UK calls for Britain’s departure to be delayed.
After the first set of talks with the Government, DUP deputy leader Nigel Dodds said the Irish backstop remained the party's "key problem".
Asked if extra cash for Northern Ireland had been discussed with Philip Hammond, Mr Dodds said: "The Chancellor of the Exchequer is obviously a key member of the Government but he is also responsible for HMRC and the whole issue of their involvement in customs and other regulatory issues is a key concern for us."
Other ministers involved in the talks included David Lidington, Michael Gove and Julian Smith, he said.
Mr Dodds continued: "We are not discussing cash in these discussion."
He said the Government was now "very focused" on addressing the issue of the backstop.
"From day one, our focus has been on the red line of how Northern Ireland is treated separately from the rest of the UK.
"That is the issue that has been the priority concern for us."
MPs backed a move to push back Brexit beyond the scheduled date of March 29 in dramatic parliamentary scenes which saw a majority of the Conservative party in the opposite lobby from the Prime Minister.
But any delay will require the agreement of the other 27 European Union members, with talks about any conditions for an extension set to begin before leaders gather at a summit next week.
European Council president Donald Tusk met Dutch Prime Minister Mark Rutte in The Hague on Friday before talks with the bloc’s key power brokers Angela Merkel, the German Chancellor and France President Emmanuel Macron on Monday.
Following the talks, Mr Rutte said the current Withdrawal Agreement is the “only deal on the table”.
On Tuesday, Mr Tusk will travel to Dublin to meet Taoiseach Leo Varadkar before the summit in Brussels on Thursday.
Mr Tusk said: “I will appeal to the EU27 to be open to a long extension if the UK finds it necessary to rethink its Brexit strategy and build consensus around it.”
But European Parliament Brexit co-ordinator Guy Verhofstadt questioned why the leaders of the 27 should grant an extension if Mrs May was “not ready for a cross-party approach to break the current deadlock” in the Commons.
The Prime Minister is set to bring her Brexit deal back to the Commons for a third meaningful vote next week, and Attorney General Geoffrey Cox has sought to provide further legal assurances about the Irish backstop.
But Mrs May’s hopes of persuading Eurosceptics and the DUP to back the deal were dealt a blow after the “Star Chamber” of Brexiteer lawyers rejected Mr Cox’s latest assessment.
The group of lawyers, led by veteran Tory Sir Bill Cash, said a suggestion that the UK could use the Vienna Convention – the international agreement that lays down the rules about treaties – to unilaterally pull out of the backstop was “badly misconceived”.
The panel of lawyers, which significantly also includes DUP deputy leader Nigel Dodds, rejected the supplementary legal advice from Mr Cox.
The Attorney General’s advice hinges on Article 62 of the Vienna Convention, which says that if there has been “a fundamental change of circumstances” following the conclusion of a treaty “which was not foreseen by the parties”, then the countries involved would be allowed to withdraw from it.
Mr Cox said: “It is in my view clear and undoubted in those exceptional circumstances that international law provides the (UK) with the right to terminate the Withdrawal Agreement.”
But the Brexit-backing lawyers said “given the high burden that a state must meet to use it, and given the extreme reluctance of international courts and tribunals to accept it”, the Vienna Convention route “supplies no assurance whatsoever that the UK could terminate the Withdrawal Agreement in a lawful manner”.