Arlene Foster has said the DUP and Sinn Fein are working hard to close the gaps between the two parties as talks to restore power-sharing continue at Stormont.
Mrs Foster stressed that decisions had to be made next month about whether the Executive could be restored, as agreement about a budget for Northern Ireland had to be in place by the end of October.
Speaking on RTE last night, the DUP leader welcomed comments last weekend by Gerry Adams about the negotiations.
The Sinn Fein president dismissed as "a lie", speculation his party wasn't interested in restoring devolution and insisted he was "up for doing a deal with the DUP".
Mrs Foster said the challenge now was to convert the change of tone into actions that would allow an executive to be formed.
She added that people in Northern Ireland wanted to see a devolved government established.
Earlier, the Secretary of State said talks between the DUP and Sinn Fein had "intensified and deepened".
James Brokenshire welcomed the improved mood at discussions between the two parties, who have a fortnight to reach agreement to form an executive.
If they fail to do so, he will move to pass a budget for Northern Ireland in the House of Commons.
Mr Brokenshire hailed the "positive statements" by the DUP and Sinn Fein in recent days and urged them to translate words into actions. An Irish Language Act remains the stumbling block to a deal, with Sinn Fein insisting on standalone legislation.
"I firmly believe a deal is doable with the right intent and focus," Mr Brokenshire said.
"We've obviously seen some more positive statements, but it is now about converting that into a deal, converting that into the formation of an executive.
"I would strongly encourage the parties to continue that intensive process and to bring that about, to make that happen and to see the restoration of devolved government that everyone wants to have and wants to see back in place."
But TUV leader Jim Allister yesterday branded mandatory coalition as "a busted flush".
He said: "If voluntary coalition is not doable, then legislative devolution - as I have previously articulated - is about the only remaining option to keep Stormont open. Though, perhaps, a Westminster Grand Committee could do as good a job?
"Traditional Unionism does not baulk at a one parliament, one people approach - indeed, at one level it is the natural outworking of being a unionist."
Meanwhile, Taoiseach Leo Varadkar said neither he nor Theresa May were contemplating failure in efforts to restore devolution.
Mr Varadkar was in London yesterday for talks with the Prime Minister in Downing Street.
He said the two of them were in a "shared space" on trying to get power-sharing up and running.
He added that he could see no advantage in holding another Assembly election in a bid to end the stalemate.
Mr Varadkar maintained it was too early to say if Britain had made enough progress in the Brexit negotiations to allow it to progress to the next phase.
A decision on that will be taken by the 27 EU leaders when they meet next month.
The Taoiseach said it would be shaped by the views of chief EU negotiator Michel Barnier. He urged the British Government to be "more specific" about the future relationship between the UK and the Republic after Brexit.
But he welcomed Mrs May's pledge that she didn't want any physical border between Northern Ireland and the Republic.
Gerry Adams urged Mr Varadkar to oppose Brexit talks moving on to the next phase, saying the UK Government had "failed to provide solutions to the key issues affecting the island of Ireland".
He added: "The Taoiseach has a duty to stand up for Irish national interests.
"It would be extremely reckless to allow the negotiations to proceed in absence of these issues being addressed in a substantive and comprehensive way."
Downing Street said the Government is working on a "practical solution" to deal with the Irish border.
A No 10 spokesman said: "The Prime Minister made clear how the UK will be the strongest friend and partner to the EU after we leave the EU and how maintaining the reciprocal arrangements for the Common Travel Area and the citizenship rights guaranteed by the Belfast Agreement were at the heart of our approach."