The cross-party discussions over Brexit on Friday ended without any agreement six weeks after they started.
Prime Minister Theresa May, who has promised to set a timetable for leaving Downing Street following a Brexit vote in June, will try once again to win the support of MPs in the week beginning June 3, when the Commons votes for the first time on the European Union (EU) Withdrawal Agreement Bill - the legislation needed to implement her deal with the EU.
Brexit had been due to take place on March 29 but after MPs voted down the deal May had negotiated with the bloc three times, the EU gave the UK an extension until October 31.
This prompted negotiations between the Tories and Labour to see if the parties could come to a Brexit agreement, despite differences over issues including membership of a customs union.
In a letter to the Prime Minister, Corbyn said the move towards choosing a new leader for the Conservative Party meant "the position of the government has become ever more unstable and its authority eroded", undermining confidence in the "government's ability to deliver any compromise agreement".
He also said that "not infrequently, proposals by your negotiating team have been publicly contradicted by statements from other members of the cabinet".
Corbyn described the talks as "detailed" and "constructive", but said "while there are some areas where compromise has been possible, we have been unable to bridge important policy gaps between us".
He said the party would "carefully consider" any proposals by the government, but that, without "significant changes", Labour would continue to oppose the "botched deal".
The Prime Minister's official spokesman said: "We have made real progress on some issues such as workers' rights and environmental protections, but it is clear that we are not going to be able to reach a complete agreement.
"In particular, there have been very challenging discussions in respect of the different positions of the two sides on customs and the holding of a second referendum."
The spokesman added that May continued "to believe it is the duty of elected politicians to deliver on the result of the referendum".
Labour's favoured plan includes a permanent customs union with the EU, meaning no internal tariffs (taxes) on goods sold between the UK and the rest of the bloc.
It also keeps the option of a further referendum on the table, giving the public a say on the deal agreed by Parliament.
Both scenarios have caused anger among Brexit-backing Conservatives, who claim a customs union would stop the UK negotiating its own trade deals around the world and who believe another public vote is undemocratic.
Some MPs have also criticized May for even entering into talks with Labour, but the Prime Minister said the government had "no choice but to reach out across the House of Commons".
Tory backbencher Simon Clarke responded to the news on Twitter, saying: "Thank God. They (the talks) ought never to have happened."
Tory MP Priti Patel, who is a 'Leave' supporter, also said many members of the party "did question the judgement of the cabinet when they approved (the) talks".
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