Northern Ireland power-sharing talks have resumed amid uncertainty about a parliamentary deal between the Tories and the Democratic Unionist Party.
Negotiations aimed at restoring the Stormont executive were previously put on hold due to the UK general election.
The deadline for an agreement to be reached has been extended to 29 June.
DUP leader Arlene Foster said her party wanted devolution up and running as soon as possible after a “constructive” meeting with Sinn Féin.
Mrs Foster is due to meet the prime minister on Tuesday to discuss the formation of a DUP-supported Conservative government at Westminster.
Sinn Féin President Gerry Adams said earlier no deal between the Conservatives and the DUP would be good for Northern Ireland.
Devolved government in Northern Ireland broke down in January and there has been political deadlock following a snap assembly election in March.
Stormont leaders are meeting Secretary of State James Brokenshire and Irish Foreign Minister Charlie Flanagan.
If no executive is formed, Mr Brokenshire has warned Northern Ireland may face direct rule.
As he went into the talks, Mr Flanagan said the Irish government had two key priorities:
- Its responsibilities as co-guarantor of the Good Friday Agreement to help with the formation of the executive
- The question of the withdrawal of the UK form the EU
Mr Brokenshire said he would continue to chair the talks, despite calls for him to be replaced by an “independent broker”.
If there was no agreement by 29 June, Northern Ireland could face direct rule, he added.
Mr Adams said Sinn Féin did not believe that “any deal between the DUP here and the English Tories will be good for the people here”.
“I think [outgoing] Taoiseach [Enda] Kenny was right when he expressed concerns about this deal directly with the British prime minister.”
Earlier, Sinn Féin’s Conor Murphy said it “would be kind to describe Mr Brokenshire as delusional”.
“His government won’t exist unless the DUP allow it to exist and the fact that they will be dependent on them conflicts him even more.”
SDLP leader Colum Eastwood said Northern Ireland politics was “in a very, very bad place”.
“If James Brokenshire thinks for one second that he can be an independent arbiter… he is absolutely wrong,” he said.
“Arlene Foster has got the British government over a barrel – we will not accept that, and the taoiseach should not accept that either.”
Leo Varadkar, the new leader of Ireland’s Fine Gael party, has said he will raise with Theresa May the importance of impartiality in the Stormont talks.
He said it was important that the two governments, as co-guarantors of the Good Friday Agreement, should not be too close to either unionism, or nationalists and republicans.
Mr Varadkar is expected to become Irish prime minister later this week in a parliamentary vote on Enda Kenny’s successor.
Analysis – Enda McClafferty, BBC News NI Political Correspondent
At Stormont today, it is likely he focus will be on political partnerships in London and not Belfast.
The DUP is up for supporting a Conservative Government but only if its demands are met.
That support will involve backing Theresa May in any confidence vote and supporting her government’s budgets.
As yet there are no details on what the DUP wants in return, but it is thought its demands will include extra cash for Northern Ireland.
But some say the real cost of a deal could be the future of power-sharing.
Sinn Féin, the SDLP and Alliance say any partnership between the DUP and Conservatives could scupper plans to restore the institutions.
It is fast becoming a game of political poker with high stakes.
The Alliance Party have echoed the SDLP and Sinn Féin’s concerns that such a partnership could make power-sharing at Stormont more difficult.
The former Labour secretary of state for Northern Ireland, Peter Hain, told BBC Radio Ulster’s Good Morning Ulster a DUP-Conservative arrangement could have a negative impact on the talks.
Under Northern Ireland’s power-sharing agreement, the executive must be jointly run by unionists and nationalists, with the largest party putting forward a candidate for first minister.
Sinn Féin’s Martin McGuinness quit as deputy first minister in January in protest against the DUP’s handling of a botched green energy scheme.
The party said it would not share power with DUP leader Arlene Foster as first minister until the conclusion of a public inquiry into the Renewable Heat Incentive (RHI) scheme.
Mr McGuinness, who had been suffering from a rare heart condition, died earlier this year.