Arlene Foster has said a deal between her Democratic Unionist Party and the Conservatives could be a "tremendous opportunity" for Northern Ireland.
She was speaking after what she called "constructive" talks with Sinn Féin about restoring power-sharing.
Devolved government in Northern Ireland broke down in January and there has been political deadlock following a snap assembly election in March.
The deadline for an agreement to be reached has been extended to 29 June.
If no executive is formed, Secretary of State James Brokenshire has warned Northern Ireland may face direct rule.
Brushing aside calls from Sinn Fein and the SDLP for him to be replaced by an "independent broker", Mr Brokenshire said the British government was "very clear" on its responsibilities to "act fairly to the benefit to all communities".
Mrs Foster is due to meet the prime minster on Tuesday to discuss the formation of a DUP-supported Conservative government at Westminster.
A senior minister has said he is "optimistic" a deal would be reached to allow a proposed Tory minority government to get its legislative programme through the Commons.
Mr Brokenshire said those negotiations were "entirely separate from our intent and desire to see devolution restored here".
But Sinn Féin President Gerry Adams said no deal between the Conservatives and the DUP would be good for Northern Ireland.
And Sinn Féin's Conor Murphy said earlier 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," he said.
But Mrs Foster rejected Sinn Fein's accusations the Good Friday Agreement would be compromised if her party entered into a deal to support a minority Conservative government.
She said her MPs had a right to participate in the government process at Westminster.
"I think this is a tremendous opportunity not just for this party but for Northern Ireland in terms of the nation, and we're looking forward to playing our part in that," she said.
But SDLP leader Colum Eastwood said Northern Ireland politics was "in a very, very bad place".
"Arlene Foster has got the British government over a barrel - we will not accept that, and the taoiseach should not accept that either."
The Alliance Party echoed the SDLP and Sinn Féin's concerns that such a partnership could make power-sharing at Stormont more difficult.
Mr Brokenshire and Irish Foreign Minister Charlie Flanagan both attended Monday's talks with Northern Ireland's five main parties.
Mr Flanagan said the Irish government had two key priorities in the talks:
- 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
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 - Stephen Walker, BBC News NI Political Correspondent
The Prime Minister will meet with Arlene Foster on Tuesday, well aware that a deal with the DUP is the only chance the Conservatives have of staying in power.
If an agreement is reached it is likely to be what is known as a confidence and supply arrangement where the DUP would support the Tories on key votes like the Queen's speech, the budget or a vote of no confidence.
Critics say the move endangers the peace process and the government will not be an honest broker in Northern Ireland.
If a deal is done it will propel Arlene Foster's party onto the national stage and give her MPs an influence they could not have anticipated during the election campaign.
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.