The Labour leader reiterated his call for Theresa May to resign as Prime Minister and said his party had achieved an "incredible result", putting on more than three million votes and gaining seats all over the UK.
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"I think it's pretty clear who won this election," he said at Labour's headquarters in central London.
"We are ready to do everything we can to put our programme into operation. There isn't a parliamentary majority for anybody at the present time, the party that has lost in this election is the Conservative Party, the arguments the Conservative Party put forward in this election have lost.
"I think we need a change."
Mr Corbyn said he would not make any coalition deals or pacts but would instead put forward Labour's own programme for government.
"We have done no deals and no pacts with anybody, we're there as the Labour Party with our points of view. Everybody knows what they are and everyone can see the huge increase in our support because of the way we conducted the election and the comprehensive nature of the programme we put forward."
Mr Corbyn mocked Mrs May's election campaign slogan that she would provide "strong and stable" leadership.
"She fought the election on the basis that it was her campaign, it was her decision to call the election, it was her name out there, and she was saying she was doing it to bring about strong and stable government.
"Well, this morning it doesn't look like a strong government, it doesn't look like a stable government, it doesn't look like a government that has any programme whatsoever."
Asked if there would now be another election, Mr Corbyn said: "Parliament must meet and Parliament will have to take a decision on what happens. When a government puts forward the Queen's Speech, we will put forward our point of view, we are of course ready to serve."
Mr Corbyn said Labour has won a "huge mandate" to challenge austerity.
Asked if the uncertainty created by a hung parliament was good for Britain, he replied: "A hung parliament is what we've been given, it's up to MPs to deal with that.
"We have a huge mandate from a huge increase in our support to carry forward a programme that challenges austerity, that challenges poverty and challenges inequality and gives opportunities for young people, for people in the middle, and gives protection for older people.
"That surely is a very important message that the people in this country, in every part of this country, have given us all today."
Shadow chancellor John McDonnell told the BBC he was "disappointed" that Labour had not secured an overall majority.
But he added: "We have laid the foundations for a minority government, and then eventually a majority government.
"The instability that we now have is not from the Labour Party or other parties, it's the Conservative Party itself.
"If we can form a minority government, I think we could have a stability government, not through deals or coalitions but policy by policy.
"That would prevent another election, because I think people have had enough of elections."
Mr McDonnell said that if Mrs May persisted in her efforts to remain in power, Labour would table an alternative Queen's Speech and seek to put it to a vote.
He said that he did not expect the Conservatives to be able to produce a stable government, with MPs calling for Mrs May's resignation and senior figures like Boris Johnson and David Davis "on manoeuvres".
"I hope she realises today, very quickly, that she cannot continue," said Mr McDonnell.
"I think the Conservative Party needs to recognise it cannot re-enter government in the way it is at the moment, in its unstable, divided form."
He said: "I'm hoping the situation will be clarified within days, otherwise we are in an impossible position with the negotiations on Brexit coming.
"The responsibility is on Theresa May now to stand down and for the Conservative Party to go away and sort itself out and let a Labour government take place."
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