The Conservatives are negotiating with the Democratic Unionist Party (DUP) to get support for their minority government.
Brexit Secretary David Davis predicted some parts of the Tory manifesto would now have to be "pruned" after the Tories lost their Commons majority.
On Monday, Theresa May was expected to face questions from her backbenchers for the first time since last week's election.
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They are expected to raise concerns about her leadership style, and press for more details on talks with the DUP.
The informal tie up with the DUP has caused concern in some quarters, with UK Greens MEP Molly Scott Cato telling this website, "Teresa May's election slogan, 'strong and stable', rings very hollow now. She has no authority and will struggle to lead a government and conduct Brexit negotiations. Relying on the DUP adds to the uncertainty."
She added, "Like her predecessor, she gambled with the country's interests to sort out internal party divisions. And like him she has come unstuck. Sadly it's people in Britain who once again will pay the economic price."
Further MEP comment came from UK Socialist Linda McAvan who said, "In their desperate desire to cling onto power, the Tories are willing to make a deal with a party that is homophobic, anti-abortion and denies climate change. It is deeply worrying that such a party could hold the balance of power at Westminster.
"Brexit has already raised huge problems for the political situation in Northern Ireland. To give one of the two main opposing parties such leverage over the UK government at a time when power sharing talks are ongoing is a completely irresponsible move."
The DUP party was established in 1971 by the Presbyterian preacher Iain Paisley, a former MEP, and has been the largest unionist party in a power-sharing government with the Irish republicans Sinn Féin for the past 10 years.
Senior DUP figures believe the Earth was created 6000 years ago, that climate change is a myth and support a return of the death penalty. It opposes same-sex marriage and has fought to halt an extension of abortion rights.
With the Tories eight seats short of an overall majority after the election, May will need to rely on the DUP's 10 Westminster MPs. Rather than entering a formal coalition, the Unionists look set to enter into a 'confidence and supply' deal with the Conservatives, giving the DUP an unprecedented role in the British government.
Party leader Arlene Foster said, "The Prime Minister has spoken with me and we will enter discussions with the Conservatives to explore how it may be possible to bring stability to our nation at this time of great challenge."
May finalised her cabinet with a small reshuffle, with Michael Gove returning to a ministerial role as environment secretary.
Gove, who took on May for the party leadership after David Cameron quit, was sacked by the Prime Minister in her reshuffle in July last year.
The Conservatives went from 331 seats to 318 in the general election, while Labour increased its number of MPs from 232 to 262.