British Prime Minister Theresa May struck a deal in principle with Northern Ireland's Democratic Unionist Party on Saturday to prop up the Conservative government, stripped of its majority in a disastrous election.
May responded that the DUP deal "would provide stability and certainty for the United Kingdom going forward", her office said. "The details will be put forward for discussion and agreement at a Cabinet meeting on Monday".
May called the general election three years earlier than required by law, with the aim of sweeping an even greater majority for her party before Brexit talks in just eight days to take the country out of the EU.
Negotiations with Brussels on the UK's departure from the European Union are due to start on 19 June, and Mrs May is now seeking the backing of the Democratic Unionist Party to prop up her minority government.
May's Conservatives lost their parliamentary majority in Thursday's vote and need the support of the 10 MPs from Northern Ireland's DUP to have a majority.
Sir Michael did not reveal what the DUP had been offered in return, but said the "outline proposal" would be published once a deal had been agreed.
Fallon said it would not be a formal coalition, instead the DUP's 10 MPs would support the government "on the big things" such as the budget, defence issues and Brexit.
"The talks so far have been positive".
Shadow foreign secretary Emily Thornberry told Sky News that the Labour party was "absolutely on our toes" to set up an alternative minority government if May's government falls apart, accusing the Conservative Prime Minister of "squatting in Downing Street".
The latest leadership speculation comes a day after two of May's closest advisers, her joint chiefs-of-staff Fiona Hill and Nick Timothy, resigned amid recriminations about their controlling management style.
Corbyn believes that without an outright majority in the House of Commons, May's position is vulnerable and he intends to vote down the Queen's Speech and table a "substantial amendment" in an attempt to bring down her administration.
Numerous key cabinet posts have already been declared as unchanged from the previous government, including Philip Hammond as Chancellor of the Exchequer, Amber Rudd as home secretary, Boris Johnson as foreign secretary, David Davis as Brexit secretary and Michael Fallon as the in-charge of the ministry of defence.
"I want to reflect on the election and why it did not deliver the result I hoped for", May said.
He said: "I am backing Theresa May".
"I have no doubt at all that Theresa May will continue to serve and work hard as Prime Minister - and do it brilliantly".
Prime Minister Theresa May dispatched her chief whip, Gavin Williamson, to Belfast on Saturday to hold talks with the DUP, which has faced criticism for its conservative views on social issues such as gay marriage and abortion. 'Supply, ' on the other hand, refers to bills required for a minority government to receive funds to allow it to enact its policies.
"I would have thought that's enough to go, actually, and make way for a government that will be truly representative of all of the people of this country", he added.
Britain's typically pro-Conservative press savaged Ms May on Saturday and questioned whether she could remain in power.