Sinn Féin has narrowed the DUP's previous 10-seat advantage to a single seat
Political parties in Northern Ireland are holding meetings with the Secretary of State James Brokenshire in a bid to form a new Stormont government.
It is understood Democratic Unionist Party (DUP) leader Arlene Foster was the first to meet Mr Brokenshire.
Sinn Féin say they are looking to meet any party willing to hold talks, while a DUP spokesperson confirmed: "The DUP met with a Sinn Féin delegation this afternoon and we agreed to meet again tomorrow."
But Gerry Adams says the party has little faith in Mr Brokenshire chairing discussions.
"If recent statements by James Brokenshire and (British Prime Minister) Theresa May are to be taken at face value, then the British government is going to make all the mistakes that it made in the past".
The SDLP, Ulster Unionists and Alliance parties are also holding talks.
It is still unclear who will replace Mike Nesbitt as UUP party leader, after he quit in the wake of a poor election over the weekend.
A new assembly must be formed within three weeks.
In last week's election, Sinn Féin cut the DUP's previous 10-seat Stormont advantage to a single seat.
The DUP now holds 28 of the 90 available seats in Stormont - but narrowly remains the largest party.
But party leader Arlene Foster has denied there is a revolt against her.
"No, there's no revolt - I'd had a very good meeting today with my party officers.
"I'll meet with my full assembly team tomorrow morning - I'm looking forward to that - and (I'll) talk to a lot of my other colleagues as well.
"So there's no problem, no problem at all".
Foreign Affairs Minister Charlie Flanagan and James Brokenshire are to meet the parties at the request of Taoiseach Enda Kenny and British Prime Minister Theresa May.
The previous Northern Ireland executive collapsed amid the refusal of Ms Foster to stand aside as first minister during an inquiry into the the botched Renewable Heat Incentive (RHI) scheme.
Sinn Féin had repeatedly called for Ms Foster to step aside, and the controversy ultimately led to Martin McGuinness resigning as deputy first minister - a decision which triggered another vote less than a year after the 2016 election.
Belfast-based journalist Alan Murray explained earlier the situation facing the DUP as they enter talks on forming a new executive.
"One MP has said that it's not impossible for Arlene Foster to stand aside," he explained. "But getting to that point where she would stand aside remains a difficulty.
"She didn't do it before the election - why would she do it after the election? [...] It leaves us in this very problematic situation of the two competing sides fighting [it] out. It's a contest to see whose will will triumph."