Speaking following his re-election as the MP for Islington North, the 68-year-old Labour leader said people had voted "for hope for the future".
Corbyn, who won his seat with more than 40,000 votes, said at the election count: "The prime minister called this election because she wanted a mandate.
"Well the mandate she's got is lost Conservative seats, lost votes, lost support and lost confidence.
With one seat left to declare - Kensington - Labour has 261 seats behind the Conservatives' 318, with the SNP on 35 and Lib Dems on 12.
Labour has taken seats from the Conservatives including Battersea and Canterbury and has unseated former Lib Dem leader and Deputy Prime Minister Nick Clegg in Sheffield Hallam. And the party made gains in Scotland included regaining ex-PM Gordon Brown's former seat of Kirkcaldy and Cowdenbeath.
But she added: "For us to have come from such a long way back, supposedly, to be in a position where we could form the next government is an extraordinary performance on behalf of the Labour Party and shows what we can do when we unite."
Thornberry was asked how Labour would able to form a minority government instead of the Conservatives and responded: "We would put forward a Queen's Speech and a Budget. Our Labour MPs would vote for it and we would call on the other parties to vote for it as well."
In the 2015 general election, Labour won 232 seats under former leader Ed Miliband, down from the 258 seats secured in 2010.
The party went into the 2017 election with 229 seats.
When Prime Minister May announced the election in April, her Conservative Party had a big double-digit lead in many polls and hoped for a landslide victory. However, the campaign saw the Tories' poll lead narrowing.
Watson said he thought Corbyn's leadership of Labour was safe. "It would be very foolish for anyone to want to stand down in the Labour Party tonight after this result.
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