Responding to reports in the Daily Telegraph that dissenting MPs are preparing to elect their own leader and launch a legal challenge for the party’s name and assets if Owen Smith fails to win the battle for the top job, Mr Corbyn branded the situation “bizarre”.
“We are getting into some fairly bizarre territory here where unnamed MPs, funded from unnamed sources, are apparently trying to challenge - via the Daily Telegraph, very interesting - the very existence of this party.
“I say to them: ‘think on, and think again’. This party was founded by brave people, pioneers who achieved a great deal, and this party has a huge membership and under the Registration of Parties Act we are the Labour Party.
“There’s no alternative, there’s no other party, we are the Labour Party, and I’m very proud to be the leader of the Labour Party,” Mr Corbyn said.
Mr Corbyn denied his leadership could trigger a split, saying: “Sorry, this is nonsense, whoever is saying my leadership is leading to a break-up of the party? Since I became leader membership has doubled, activity has increased.”
Shadow chancellor John McDonnell urged Mr Smith to condemn “the minority of MPs supporting his campaign who are threatening to subvert the outcome of this election and cause enormous damage to the Labour Party”, but the leadership challenger responded by insisting he would not “indulge in gossip”.
“This leadership process is now entirely about Labour members and supporters. We have a one member, one vote system, so MPs will have the same amount of say as all Labour members - exactly as it should be,” Mr Smith said.
The spat came as Mr Smith took his battle to topple Mr Corbyn into “enemy territory” with a campaign push in Liverpool.
With the Smith camp seeing the city as a Corbyn stronghold, they want the move to underline the would-be leader’s aim to try to reunite the party around him.
Mr Corbyn was holding rallies in Hull and Leeds as the two men continued to slug it out for the Labour crown before the winner is declared at the end of September.
The pitches came as former shadow cabinet member Angela Eagle warned Labour MPs to moderate their language after Mr Smith was forced to apologise for controversial comments aimed at Prime Minister Theresa May.
Mr Smith, who toppled Ms Eagle as the “unity” candidate tasked with ousting Mr Corbyn as Labour leader by dissenting MPs, drew widespread criticism for saying he wanted to “smash” Mrs May “back on her heels”.
Ms Eagle told The Guardian: “He should have, and has, apologised. As someone that has heard cruel words spoken about me, I know that language matters. And we’ve all got a responsibility to be sensitive with our use of language.
“Owen has shown a capacity to recognise, and apologise for, insensitivity, and that’s important.”
The visit to Liverpool by Mr Smith sees him attending the city’s gay pride celebrations, and meeting party members at a special event.