Democratic Unionist leader Arlene Foster has welcomed comments by Sinn Féin leader Gerry Adams who said he was committed to restoring power-sharing and rejected any suggestion his party had given up on Stormont.
Mrs Foster said the challenge now is to translate the change of tone into actions that will allow the formation of an executive.
She told RTÉ News there are still gaps in the ongoing talks between the DUP and Sinn Féin, but they are working hard to close them because she believes people want to see the return of devolved government.
She said she believes decisions have to be made in October about whether power-sharing can be restored, because agreement about a budget for the different departments has to be in place by the end of next month.
Meanwhile, Northern Ireland Secretary James Brokenshire has said that talks between Sinn Féin and the DUP aimed at saving power-sharing have "intensified and deepened".
He welcomed what he characterised as "positive statements" from both parties over the weekend and urged both to convert those words into action.
While both the DUP and Sinn Féin issued statements yesterday stressing their commitment to restoring a devolved executive, there has been no public indication whether either side has given ground on the roadblocks currently preventing it.
Mr Brokenshire has already warned the region is on a "glide path" to a form of direct rule from London if the long-running impasse that triggered the collapse of power-sharing at the start of the year is not resolved by the middle of next month.
The Conservative MP gave his assessment on the state of the troubled negotiation process, saying "I firmly believe a deal is doable with the right intent and focus.
"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 and 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."
The DUP's refusal to sign off on a Sinn Féin demand for a free-standing piece of legislation that would enshrine statutory protections for Irish speakers is one of the key obstacles preventing the re-establishment of a coalition executive in Belfast.
While the DUP is prepared to countenance legislative protections for Irish as part of a wider piece of legislation that also incorporates the Ulster Scots culture, the party is set against a free-standing Irish language act.
Formal roundtable talks involving the five main Stormont parties and the British and Irish governments have still not resumed after they were parked for the summer.
Sinn Féin and the DUP are instead engaged in a series of private meetings - discussions that are due to continue this week.
Mr Brokenshire said there had been a change in pace of that bilateral process.
"That has intensified and deepened and I warmly welcome that," he said.
In response to Mr Adams's comments yesterday, DUP MLA Simon Hamilton welcomed as a "step forward" what he described as a "change of tone".
DUP deputy leader Nigel Dodds said it would be a mistake to suggest they were on the verge of a massive breakthrough, but they continued to work at it.
He said there could only be substantive progress if people moved forward on the basis of a shared future, not on the basis of Sinn Féin demanding that all their wishes be met without respect for other people's point of view.
"We will continue to work at the process of trying to get a government set up for Northern Ireland.
"We think that is in the best interests of Northern Ireland, we are up for that, we would form the government today.
"If others are showing some more flexibility I welcome that, I hope they do that in substantive terms as well."