The Democratic Unionists saw their ten-seat lead as the biggest grouping at Stormont cut to just one following Thursday’s election.
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.
Asked yesterday 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.”
Following Thursday’s election, Sinn Fein closed the gap on the DUP to a solitary seat while the overall unionist majority at Stormont was lost.
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 a botched green energy scheme predicted to cost the Northern Ireland taxpayer close to half a million pounds.
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.
Mrs Foster established the failed green energy scheme.
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.