He dismissed the prime minister’s offer to meet him and other party leaders – to discuss the way ahead after her deal was rejected by MPs – as a “stunt”.
And he said Labour would table further no-confidence motions in the government “if necessary”.
In a direct message to Mrs May he said: “Take no-deal off the table now please prime minister.”
The prime minister has held talks with senior figures from the SNP, the Lib Dems, the Green Party and Plaid Cymru after she narrowly survived a no-confidence vote on Wednesday.
She is to publish an updated plan of action on EU withdrawal to Parliament on Monday, 21 January, with a full debate and the key vote on it scheduled for Tuesday, 29 January.
In a speech in Hastings, a marginal constituency currently held by Work and Pensions Secretary Amber Rudd, Mr Corbyn said that after Tuesday’s vote it was “clear that her EU deal is now finished”.
“There can be no question of tweaks or sweeteners from Brussels to bring it back to life.”
He said that to get a deal that could get the backing of MPs, Mrs May had to “ditch the red lines and get serious about proposals for the future”.
Mr Corbyn said Labour would table an amendment on its own Brexit proposals on Monday, which are based around “three pillars”:
- permanent membership of a customs union with the EU
- a “strong single market relationship”
- guarantees to “at least keep pace” with EU standards on workers rights, and environment and consumer protections
The Labour leader is coming under pressure from dozens of his own MPs to back calls for another EU referendum.
Mr Corbyn said his preferred option remained a general election “to break the deadlock and find a solution that works for the whole country”.
“That is why I tabled a motion of no confidence last night – and we will come back on it again if necessary,” he told the audience of Labour members.
But he added: “If the government remains intransigent, if support for Labour’s alternative is blocked for party advantage and the country is facing the potential disaster of no-deal, our duty will then be to look at other options, which we set out in our conference motion, including that of a public vote.”
He declined to say what Labour’s position would be in such a vote.
“If a second referendum should take place, then obviously the party will decide what role we will play in that and what our view would be.
“But I can’t really go along with the idea it should simply be a re-run of what happened in 2016.
“There has to be a discussion about the options that we put forward and we’ve put forward the three options that I’ve outlined.”
He also suggested Article 50, the process taking the UK out of the EU on 29 March, might have to be extended if an agreement could not be reached in time.
The Labour leader has set out his demands in a letter to Mrs May, in which he tells the prime minister: “I am disappointed that there have already been several briefings in which you continue to rule out a customs union.
“A new customs union is part of a solution favoured by most businesses and trade unions and one that I believe could command a majority of the House of Commons.”
But some Labour MPs who have been critics of him are urging a change of stance:
And Labour MP Luciana Berger, a member of the People’s Vote campaign for another referendum, said: “After the vote of confidence was defeated, we now know a general election is off the table and any chance of Labour negotiating its own Brexit deal has gone.”
She said her party now needed to “listen to its members and voters” and “follow its democratically-agreed conference policy of campaigning for a new public vote”.