Former chancellor George Osborne described it as a "catastrophic" result while another Conservative MP said: "She needs to go".
The moves buy May a temporary reprieve.
If the Conservatives can secure 316 seats or more, the DUP's gains in Northern Ireland are enough to prop up Mrs May's government bid.
Its key slogan during the campaign turned out to be rather prescient: "A vote for the DUP team is a vote to send "Team Northern Ireland" to Westminster".
Downing Street said an outline agreement on a "confidence and supply" arrangement had been reached which will be put to the cabinet for discussion on Monday.
With 649 of 650 seats in the House of Commons declared, the Conservatives had 318 - short of the 326 they needed for an outright majority. The main opposition Labour Party surpassed expectations by winning 262.
They were replaced by Gavin Barwell, a former housing minister who lost his seat in the election.
On the same website Ms Hill said: "I have no doubt at all that Theresa May will continue to serve and work hard as Prime Minister and do it brilliantly".
And Ukip leader Paul Nuttall fell on his sword after just six months in the job, after slumping to a distant third place in Skegness & Boston on a woeful night for the Eurosceptic party, which shed swathes of voters to Labour and Conservatives.
Martin Selmayr, senior aide to European Commission President Jean-Claude Juncker, responded to the resignations by tweeting the word "bauernopfer" - German for the sacrifice of a pawn in chess.
She insisted she would press ahead with Brexit talks, which are to begin in 10 days. That could cheer opponents of a "hard Brexit" that would take Britain completely out of the single market and the customs union.
It added that "the logic leading to Mrs".
Presidency: Peace comes only through a Palestinian state
Today, around 600,000 Jewish settlers live in 140 settlements in occupied East Jerusalem and the West Bank. The 1948 exodus came to be known by the Palestinians as "the Nakba" or "the Catastrophe".
He has also previously claimed he would seek to form a minority government if the Conservatives failed to secure a Commons majority.
Speaking after visiting Buckingham Palace on Friday, she said only her party had the "legitimacy" to govern, despite falling eight seats short of a majority, the BBC reported.
Later, at a news conference, Ms Foster said the DUP would go into talks with the Conservatives, with the future of the Union as "our guiding star".
Northern Ireland is the only part of the U.K.in which same-sex marriage is illegal.
But Labour said they were the "real winners".
DUP leader Arlene Foster confirmed that she had spoken to May and that they would speak further to "explore how it may be possible to bring stability to this nation at this time of great challenge", the BBC reported.
"In particular, I regret the decision not to include in the manifesto a ceiling as well as a floor in our proposal to help meet the increasing cost of social care".
Johnson denied the reports as "tripe" and said: "I am backing Theresa May". "When it becomes a matter for me is when people try to redefine marriage".
For example, the party once appointed a climate change denier as the Northern Ireland environment minister and has a number of creationists - those who believe the universe and all organisms were formed by divine creation - as senior leaders.
The result was a personal humiliation for Mrs May who called the election three years before she had to to bolster her position in Parliament as she embarked on the negotiations on Britain's withdrawal from the EU.
Newspaper headlines saw her as just clinging on.
Comments