Denying the reports, Mr Corbyn told BBC Breakfast that speculative stories belonged on “imadeitupyesterday.com”.
Calling claims he was considering stepping down amid allegations he is damaging his party “absolute nonsense”, he added: “I’m really surprised the BBC is reporting fake news. There is no news. There is no news.”
The phrase “fake news” has popular with Donald Trump, who routinely uses it to refer to unfavourable coverage by the “mainstream media”. Theresa May also used one of her new US ally’s sound bites during Prime Minister’s questions on Wednesday, accusing Labour of peddling “alternative facts”.
The Labour Party is facing a fresh wave of defiance from the front bench over Brexit, with Clive Lewis quitting as shadow Business Secretary to defy a three-line whip to oppose the European Union (Notification of Withdrawal) Bill. He joined 51 of his Labour colleagues to vote against the Government, while 13 abstained.
Conservatives seized on Labour's turmoil over the vote to to claim the Opposition was “hopelessly divided”.
Asked about the rebellion by some of his MPs, Mr Corbyn said: “No, it's not a disaster.”
Pressed about claims that he would have to reconsider his position in a year if his poll ratings had not improved, Mr Corbyn replied: “We are demanding social justice in Britain. That's what the Labour Party exists for, that's what I'm leading the party for and that's what I'm going to continue doing.”
The vote on the Brexit Bill was widely regarded as a victory for Theresa May who many believe wishes to impose a hard Brexit.
It will now need to be approved by peers before the Prime Minister can begin exit talks under Article 50 of the EU treaties, which she has promised by April.
A Government source has stressed the Lords will face an "overwhelming public call to be abolished" if it attempts to frustrate the progress of the legislation. And David Davis told unelected peers not to try to change the simple two-clause Bill as it was passed by MPs unamended, which he said "reflected the will of the people".
The Liberal Democrats have vowed to continue trying to amend the legislation after it comes to the Lords on 20 February to ensure a second referendum on the final exit deal achieved by Ms May. Pro-Europe Tory and Labour peers may also try and make changes to the Bill.
In January, the BBC Trust ruled that the BBC's political editor, Laura Kuenssberg, inaccurately represented Mr Corbyn's views on shoot-to-kill policies in the aftermath of the Paris attacks.
A viewer complained to the Trust about the November 2015 News at Six report on security measures being considered by the British Government in the wake of the attacks.
Ms Kuenssberg said that she had asked the Labour leader whether he would support a shoot-to-kill policy if a similar attack happened in London, and if he were Prime Minister. The footage showed Mr Corbyn responding: “I’m not happy with a shoot-to-kill policy in general. I think that is quite dangerous and I think can often be counter-productive. I think you have to have security that prevents people firing off weapons where you can."
The viewer said this was misleading because no reference had been made to the Paris attacks when Mr Corbyn had been asked about the issue. They claimed it was "in order to cause Mr Corbyn maximum political damage".
Trustees rejected the idea there was a "deliberate attempt to mislead audiences", but said the broadcast was "not duly accurate" because it presented "an answer Mr Corbyn had given to a question about 'shoot to kill' as though it were his answer to a question he had not in fact been asked".
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