The UK and Irish prime ministers have agreed the gap between DUP and Sinn Féin is "narrow" after the latest talks broke up without a deal.
The DUP and Féin blamed each other for the failure to restore power-sharing, before the UK government said it had to step in to set a new Stormont budget.
Theresa May spoke by phone to Irish PM Leo Varadakar after the failure of the latest round of talks on Wednesday.
The NI Secretary is to lay out his plans for a budget to MPs later.
James Brokenshire had set this week as a deadline for the parties to either reach agreement to return to government or face further intervention.
'No direct rule desire'
In their call, the PMs agreed there was still time to reach a deal to form an executive.
The DUP and Féin have both said they are prepared to take part in more talks, but as yet, none are planned.
An Irish government spokesman said that during the phone call, Mr Varadakar made the point that there could be no return to direct rule from Westminster, as it existed prior to the Good Friday Agreement.
The taoiseach told Mrs May that the various provisions of the 1998 agreement would have to be honoured.
Mrs May replied that she did not want to see a return to direct rule and that moves to implement a budget were not the first step on that road, added the spokesman.
On Wednesday, Mr Brokenshire said action was necessary at this point because Northern Ireland's public service would begin to run out of resources by the end of this month.
"No government could simply stand by and allow that to happen," he said.
The secretary of state added that he would be ready to withdraw the budget bill if an executive is formed before December.
Sinn Féin said the latest talks had "ended in failure" but added that it was prepared to resume negotiations.
The party's Stormont leader Michelle O'Neill said her party had tried to be "flexible", but "endless talks without conclusion are not sustainable".
The DUP said progress towards a deal has been held up by Sinn Féin's "narrow political agenda".
Its leader Arlene Foster said Mr Brokenshire's decision to go ahead with a budget did not mean negotiations to restore the Stormont executive were over.
She told Irish broadcaster RTÉ: "It's right that he moves ahead with that, but that doesn't stop us continuing to engage with Sinn Féin in trying to find a solution to the problems that we have."
Analysis: Stephen Walker, BBC News NI political correspondent
Questions are being asked by both parties about whether their rival negotiators are interested in striking a deal.
Sinn Féin president Gerry Adams thinks the DUP has not engaged in a serious way about his party's desire to see an Irish language act and provision for same-sex marriage.
For its part, the DUP has always insisted Sinn Fein has put too many barriers in place and introduced too many red lines.
Some think Mr Adams is more interested in matters south of the Irish border than in a restoration of devolution at Stormont.
Unless the atmosphere changes, there is little sign the discussions can be fruitful.
The DUP and Sinn Féin have failed to reach an agreement in spite of numerous rounds of discussions since March's assembly elections.
The vote was called after the Northern Ireland Executive collapsed amid a bitter split over the handling of a botched renewable energy scheme in January.
Sinn Féin's demand for legislation to give official status to the Irish language has become one of the main stumbling blocks in negotiations to restore the executive.