The DUP, Sinn Féin, the UUP, Alliance and the SDLP will hold separate meetings with Theresa May.
'Although I don't expect it suddenly to collapse, because there's a broad consensus that wishes it to continue, I think we have to take care with it and take care that everything we do does not exaggerate the underlying differences that still are there in the Northern Ireland community'.
Thursday's talks will focus on attempts to restore devolution at Stormont by the end of this month.
The leader of Britain's House of Commons says the state opening of Parliament will take place on June 21.
An agreement between the Tories and DUP is thought to be close, with Mrs May saying the talks had been "productive" and emphasising the need for "stability" in government.
The deal is now not expected to be announced before next week. However, Major, as with many other critics of the deal, argued that other devolved governments in the United Kingdom would be angered by a promise of extra funding for Northern Ireland.
The DUP, or the Democratic Unionist Party, are one of two main parties in Northern Ireland.
Energized by the historic outcome, Corbyn, who still remains in minority, has called on May to step down and clear the way for him to lead the UK's exit from the European Union (EU).
Scottish Conservative leader Ruth Davidson, who wields considerable influence after the Scottish Tories won 13 seats, said: "I want to ensure that we can look again at issues like Brexit which we know we are now going to have to get cross-party support for".
She waved to reporters but would not be drawn on whether a deal would be agreed on Tuesday.
"Any deal which undercuts in any way the process here or the Good Friday Agreement is one which has to be opposed", he said.
"The only way they could be sure of what the other's intentions were was trusting me to be right when I told them that it was my view that, for example, if Sinn Fein did a certain thing, then Ian Paisley would agree to join the government".
To do so, she will be heavily reliant on the 10 lawmakers from the eurosceptic DUP, who can help her edge past the 326 votes needed in Parliament to avoid the collapse of the government.
She said: "As we welcome new members on all sides, we should celebrate the fact that we have a record number of MPs from Black and Minority Ethnic backgrounds, including a female Sikh MP, we also have more disabled MPs and more LGBT MPs".
The late deputy first minister, Martin McGuinness, stood down to protest the DUP's handling of an energy scandal, in a move that triggered a snap election.
Permission for new grammar schools is also out of the Queen's Speech, but that's despite the DUP - which likes grammars - and simply because quite a lot of Tory backbenchers (hello Nicky Morgan) don't like them.
Downing Street sources told our correspondent talk of a delay in announcing a deal was "not coming from us".
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