The Democratic Unionist party is to continue intensive talks to try to reach an agreement to allow it to back Theresa May’s Brexit deal, with discussions focusing on domestic legal guarantees that Northern Ireland will have no regulatory divergence with the rest of the UK.

Downing Street is hopeful that the support of the DUP is key to unlocking the backing of many Conservative Brexiters when May brings her deal to the House of Commons for the third time.

The DUP’s Westminster leader, Nigel Dodds, said discussions were “friendly and constructive” at a Cabinet Office summit with cabinet ministers, including May’s de-facto deputy David Lidington, the environment secretary, Michael Gove, and the chancellor, Philip Hammond, sparking speculation that a financial incentive for Northern Ireland could be part of the negotiations.

Dodds said Hammond had been present at the meeting to discuss the role of HMRC, customs and regulations and denied it had been to discuss extra spending.

“I would not read anything in that the chancellor was there other than he is a senior member of the government who is clearly involved in many of the issues we are talking about,” Dodds said. “We are not discussing cash in these discussions; this is about Brexit and how we protect the future of the United Kingdom and protect Northern Ireland’s economic and political future.”

Talks are expected to continue into the weekend and are likely to cover the role of any future Northern Ireland assembly if the Irish backstop were used – one of the issues senior DUP leaders have asked for further clarification about. Ministers are aware the DUP will try to exact maximum concessions.

Dodds has been particularly vocal that May’s government has not faithfully implemented what was agreed and included in paragraph 50 of the joint report in December 2017, which stated the assembly would have a veto over any new regulatory difference.

“A lot will depend on what the government is able to do to provide those guarantees that are necessary to assuage our concerns,” Dodds said after the meeting.

“We have pointed previously to our concerns that the government has deleted so far the paragraph 50 of the December joint report, which gave a lock and a provision for Northern Ireland in terms of what might happen in the backstop and the overall situation of the economic integrity of internal market of the United Kingdom.”

One former cabinet minister said that in order for the ERG to climb down and support May’s deal at the third time of asking, “there’s an unlock requirement – and that’s the DUP – and their primary concern is that they will be separated from us”.

Options under discussion include inserting into domestic law, perhaps as part of the withdrawal agreement implementation bill, the promise that Northern Ireland would be given a veto on any new barriers in the Irish Sea.

The government promised a “strong role” for the currently defunct Stormont assembly if the Brexit backstop was triggered, in a document setting out reassurances ahead of the first meaningful vote.

Dodds said at the time that the promises were “cosmetic and meaningless” and that the proposals made it plain Stormont would never be able to “override” the backstop as it would be part of an internationally binding treaty.

In an interview with the House magazine, Dodds said he felt the pressure of the negotiations “very intensely”, and that he was “in the business of wanting to get a deal done”. He said the removal of paragraph 50 was “something they should address now. That’s a pretty important area that they must look at.”

The prime minister is widely expected to bring her deal back for a third meaningful vote next Tuesday, but will not do so unless she believes the vote is winnable. That would mean convincing 75 MPs to switch their votes.

May has said there will be a short technical extension to article 50 if the deal passes on Tuesday but, if it does not get the backing of MPs, she will ask for a much longer extension, which will include taking part in the European elections and holding indicative votes in parliament on a variety of Brexit outcomes.

The Brexit secretary, Steve Barclay, who was among eight cabinet ministers to vote against the prospect of delaying article 50 in a free vote on Thursday, strongly hinted that he would resign if the deal did not pass and May sought a longer extension.

“We need a deal, we need to get that over the line. But if we don’t have a deal, we should leave with no deal. That’s always been my position and I voted as the constituency would expect,” he told the BBC. “If we can get the deal through as I hope we still will we will now need a short technical extension, but if not we shouldn’t be afraid to leave with no deal.”

Separately, the former work and pensions secretary Esther McVey, who resigned over May’s deal, has dropped a heavy hint that she could support it next week after parliament voted to extend article 50 – potentially for a long period.

“The element now is that people will have to take a bad deal rather than no deal,” she told the BBC’s Political Thinking podcast. Asked whether there was a chance she could vote for the deal next week, she said: “Yes.”