May says it's "a Cabinet that reflects the wealth of talent and experience across the Conservative Party" and "a government that is going to be governing for everyone". "The votes aren't there now in the (House of) Commons for taking Britain out of all the economic arrangements we have with the European Union", he said.
May had repeatedly ruled out the need for a new election before changing her mind.
Party insiders are placing bets on how long May will last, less than a year after Britain's surprise referendum decision propelled her into Downing Street.
Standing outside 10 Downing St. today, Britain's Prime Minister Theresa May tried to put a courageous face on the disastrous results of Thursday's vote. The DUP, although it wants to leave the European Union, will insist on keeping the single market that allows the free flow of goods across the UK's border with Ireland.
Labour gained 30 seats to win 262, with 40 percent of the vote compared to 42.4 percent for May.
"I think there is concern about the policies of the DUP, the domestic policies in Northern Ireland, but I think it's pretty clear that any arrangement that is reached is not going to be a full coalition", he told BBC Radio 4. "So whether they can hold a weak leader in place - tactically, as it were - until they are ready to move, I don't know".
The stunning outcome leaves May battling to unite different factions in her party and reliant on a handful of Northern Irish parliamentarians just nine days before Britain starts the tortuous process of negotiating its departure from the EU.
Meanwhile, Labour, which had been written off by critics as all but unelectable, surged to 261 seats, up 29 from its tally in the 2015 election.
Jonathan Powell said a deal with the DUP would jeopardize the Good Friday Agreement.
'One of them is country, one of the others is LGBTI rights and I asked for a categoric assurance that if any deal was done with the DUP there would be absolutely no rescinding of LGBTI rights in the rest of the United Kingdom and that we would try to use any influence that we had to advance LGBTI rights in Northern Ireland. She has said she favours retaining the greatest possible level of access to Europe's single market.
With Home Secretary Amber Rudd, Brexit Secretary David Davis, and Defence Secretary Sir Michael Fallon all retaining their posts, there was speculation any reshuffle could be limited to replacing the eight ministers who lost their seats in the election.
The TV channel said Foster had told them she would be travelling to London to meet May at her official Downing Street residence on Tuesday.
Victory would have been Labour's with more time, says McDonnell.
When asked about her future, senior Conservative lawmaker Owen Paterson said "Let's see how it pans out". I think she will have to go, unfortunately.
Several newspapers said Foreign Secretary Boris Johnson was being urged by supporters to launch a leadership challenge, but he dismissed the reports as "tripe" in a tweet saying he was backing May.
May's co-chiefs of staff, Nick Timothy and Fiona Hill, handed in their resignations on Saturday following the disastrous election.
The same is expected at prime minister's questions when he will face May across the dispatch box on Wednesday. And eventually Harold Wilson managed to form a government.
May had called the election to build upon her majority; instead, the party lost it.
Among Tory MPs there was anger at the way a 20-point lead in the opinion polls when she called the election in had been squandered in the course of a campaign which was widely condemned as flat-footed and uninspiring.
"I think its quite possible there'll be an election later this year or early next year, and that might be a good thing, because we can not go on with a period of great instability", he told the BBC's Andrew Marr on Sunday.