Labour won 262 seats in the General Election, up from the 232 secured by Ed Miliband in 2015, but the Conservatives remain the largest party in Parliament.
Mrs May today secured an outlined agreement with the DUP who she hopes will be able to prop up her minority in the Commons.
But Mr Corbyn said that, without an outright majority, Mrs May’s position is vulnerable and he has outline his intention to oppose the Queen’s Speech in an attempt to bring down her administration.
He told the Sunday Mirror: “I can still be prime minister. This is still on. Absolutely. Theresa May has been to the palace. She’s now attempting to form a government.
“She’s then got to present a programme to Parliament. There’s a possibility of voting the Queen’s Speech down and we’re going to push that all the way.
“We have got a mandate to deal with issues of poverty, justice and inequality in Britain. We want to end austerity and invest in this country and that’s what we’re going to do.
“Nearly 13 million people voted for us to do it. That’s why I’m here.”
Mr Corbyn said: “I don’t think Theresa May and this government have any credibility.
“The Prime Minister called this election on the basis she would need a stronger mandate to negotiate Brexit.
“Well look what’s happened. The parallels are with 1974. The Conservatives sought, as they have done this time, a ‘who governs Britain?’ mandate.