Jeremy Corbyn, who many thought was totally unelectable, took a massive chunk out of the Conservative majority.
The Tory veteran has said she has no intention of standing down and has been informally backed by the DUP.
Chancellor Philip Hammond, Foreign Secretary Boris Johnson, Home Secretary Amber Rudd, Defence Secretary Michael Fallon and Brexit Secretary David Davis have all been kept on in their roles.
The talks, which the European Union wants to ensure a legally smooth British departure, would be more uncertain without a strong negotiating partner, he said.
Tusk added on Twitter: "We don t know when Brexit talks start". The party also suffered shock defeats in the south eastern city of Canterbury, which had been a safe Conservative seat since 1918. "Do your best to avoid a no deal as result of no negotiations".
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'With a weak negotiating partner, there's a danger that the negotiations will turn out badly for both sides'.
In a statement outside No 10, the Prime Minister sought to strike a tone of business as usual.
Corbyn also said there's enough opposition in Parliament and in May's own party to topple the government.
Many in the party believe she has been fatally wounded.
58 people missing and presumed dead after London tower fire
People cast shadows as they read a message board placed near Grenfell Tower in London , Saturday, June 17, 2017 . They say they will also use visual elements like tattoos, scars and medical implants in the painstaking process.
According to Britain's best-selling Sun newspaper, senior members of May's own Conservative Party had vowed to get rid of her, but made a decision to wait at least six months because they were anxious that a leadership contest now could propel Corbyn into power.
"Mayhem" screamed the headline on the front page of The Sun, Britain s biggest selling newspaper that is normally sympathetic to the Conservatives.
Labour, the Liberal Democrats and the SNP, who are likely to have mopped up the votes between them, would have outnumbered the Tories and are likely to have defeated the PM in a Queen's Speech vote, paving the way for a coalition led by Mr Corbyn. "This is a very bad moment for the Conservative Party, and we need to take stock", Conservative lawmaker Anna Soubry said. "Brussels will be licking its lips", it said. Once again, voters have sprung a surprise. The support obtained by Labor party members contrasted with the negative predictions of hardly two months ago, when they were 20 percentage points below the conservatives in terms of intention to vote.
Despite campaigning against Brexit, Labour has accepted the result but said it would prioritise maintaining close economic ties with the EU.
"I will now form a government - a government that can provide certainty and lead Britain forward at this critical time for our country", she said. But the discussion on Twitter, as well as the parallels to what the Labour Party did overseas, could eventually mean something for a Democratic Party that's still doing some soul-searching in the early days of the Trump administration.
German minister sees hope of 'soft' Brexit
Northern Ireland does not want a Brexit that puts customs posts on its border with the Irish Republic, an European Union member. It is expected talks will take place once a month in Brussels as they work through the issues to be resolved.