Arlene Foster has denied there is a revolt in the DUP.
It comes after this newspaper reported on a possible revolt within her party as a third of MLAs wanted her to step aside to save the institutions.
The DUP saw their 10-seat lead as the biggest grouping at Stormont cut to just one following Thursday's election after Sinn Fein's surge at the polls.
Mrs Foster also said she was going into negotiations between the five largest parties on restoring power-sharing wanting to do a deal.
Sinn Fein has vowed not to re-enter devolved government with her as first minister.
Senior DUP sources told the Belfast Telegraph that Mrs Foster should reconsider her decision and not put her personal pride before what was best for "the party and the people of Northern Ireland".
Speaking to the media on Monday the DUP leader said her party received the largest ever mandate in an Assembly election and that people wanted to see the return of devolution.
Asked about her support within her party, she said: "There is no revolt.
"I've had a very good meeting today with my party officers. I'll meet with my full Assembly team tomorrow morning and talk to a lot of my other colleagues as well.
"So there's no problem, no problem at all."
Mrs Foster also said she would not be stepping aside as leader as her party entered into the talks process.
The parties have three weeks to broker a deal to resurrect the Executive.
"We're not drawing red lines," she told assembled Press outside Stormont.
Meanwhile a DUP spokesman said: "The DUP met with a Sinn Fein delegation this afternoon and we agreed to meet again tomorrow."
It comes as the Alliance party said there needed to be a "patch" solution to allow enough time for the talks process.
The election was called after former deputy first minister Martin McGuinness resigned in protest at Mrs Foster's refusal to stand aside as first minister while a public inquiry is held into the botched Renewable Heat Incentive scheme which is predicted to cost the Northern Ireland taxpayer close to half a million pounds.
Mrs Foster established the failed green energy scheme.
His resignation forced a snap election.
Northern Ireland Secretary James Brokenshire has been meeting Stormont party leaders in an attempt to persuade them to form a new power-sharing executive.
The parties have three weeks to overcome their differences.
Sinn Fein president Gerry Adams said Prime Minister Theresa May and Mr Brokenshire were "part of the problem" and called for an independent chair of the talks.
The Sinn Fein leader accused the UK Government of breaking past agreements aimed at stabilising the Stormont institutions.
He also said republicans had no confidence in Mr Brokenshire to chair post-election negotiations.
But despite the controversy, the DUP's vote was up in every constituency across Northern Ireland.
Mrs Foster said: "That is a pretty good basis on which to continue as DUP leader."
Her party's performance was overshadowed by what unionists described as a "tide" of republican support.
DUP deputy leader Nigel Dodds said it was the biggest vote ever cast for any party in an Assembly election and it would be "perverse" to suggest someone should step aside as a result.
"The people will decide who leads the DUP. The people have given a resounding mandate and endorsement to Arlene as the leader of the DUP."