Arlene Foster said she was delighted with the support she had received from her colleagues following a party meeting on Tuesday,
The DUP leader said that she was looking forward to going into the negotiations to "get a good deal, not just for unionism but for all the people of Northern Ireland".
"We are focused on the restoration of devolution and making sure that we have that stability for the people of Northern Ireland," she added.
Mrs Foster's position as leader of the DUP looks secure for the time being despite reports of dissent within her party ranks.
last night she insisted there was no revolt following Friday's shock election result in which Sinn Féin enjoyed an unprecedented surge in support.
But when questioned on republicans' insistence that they could not accept her as first minister until she is cleared of any wrongdoing over the Renewable Heat Incentive (RHI) scandal, Mrs Foster did not rule out the prospect of stepping aside to enable the restoration of the executive.
She said Sinn Féin had made it a "red line" and that it was a matter for republicans.
"We're not drawing red lines," she said.
"We want to see the negotiations working for the people of Northern Ireland."
Just one seat now separates the assembly's two biggest parties after Sinn Féin held 27 of its 28 seats in a slimmed-down chamber but the DUP suffered 10 losses.
The result also means that for the first time in Stormont's history unionism no longer holds a majority, with just 40 of the 90s MLAs now designated unionist.
The outcome has fuelled speculation about Mrs Foster's future as DUP leader but the Fermanagh-South Tyrone MLA was yesterday defiant.
Flanked by deputy leader Nigel Dodds under Carson's statue following a meeting with the secretary of state at Stormont House, she said she was going into the fresh round of negotiations wanting to do a deal.
Asked about reports of disquiet within her party, Mrs Foster 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."
The DUP leader said she wanted to see her party's mandate respected and devolution restored at the earliest opportunity.
She rejected claims that the election was a disaster, pointing out that the DUP's vote was up in every constituency across the north.
"That is a pretty good basis on which to continue as DUP leader," Mrs Foster said.
Mr Dodds said the DUP had secured 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 North Belfast MP said.
"The people have given a resounding mandate and endorsement to Arlene as the leader of the DUP."
Reports have also suggested concerns within the DUP about the role of special advisers, some of whom found themselves embroiled in the RHI controversy.
The News Letter yesterday reported that a DUP source had complained that senior adviser Timothy Johnston, who has worked alongside Ian Paisley, Peter Robinson and Mrs Foster, had been given too much authority and was effectively running the party from behind the scenes.
Meanwhile, Alliance leader Naomi Long yesterday ruled herself out of the justice minister's job in the new executive, which has previously been filled by former leader David Ford.
The East Belfast MLA said she wished to concentrate on her role as party leader.
