The threat of a Labour split dominated an increasingly bitter battle for the leadership as Jeremy Corbyn branded talk of a breakaway parliamentary party "bizarre".
After reports 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 top job, Mr Corbyn insisted they would never be able to take the Labour name.
"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".
Mr Smith, campaigning in the Corbybn stronghold of Liverpool, insisted he was fighting for the leadership in order to prevent a split as the party was now on the edge of a "precipice".
"It would be a total disaster for working people in this country if the Labour Party, the party that's been on their side for 100 years or more, were to split. Absolute disaster.
"I'm refusing even to contemplate that happening. I'm standing in order to unite the party and stop the split from occurring," he told ITV News.
Mr Smith told the BBC: "I do worry about there being a split. I say this very seriously, I think the Labour Party is standing on the edge of a precipice right now."
Mr Corbyn said he and the shadow chancellor engaged in a "Super Saturday" of grassroots campaigning across the country.
The outcome of the leadership election will be announced on September 24.