Jeremy Corbyn has warned senior figures in the Labour party that they underestimate the "huge levels of public support" for his campaign.
Speaking at a rally in central London, Corbyn also rubbished claims that he does not want to be prime minister.
He told supporters: "Why would I be here, why would our campaign be here, if we didn't want to win this campaign, in order to make the Labour Party a more effective campaigning organisation, in order that we can win the 2020 election?"
Responding to claims of plots among opponents to stop him winning, he said: "I do not think anyone should pull out. They have been nominated, they are valid candidates.
"If others want to debate arcane procedures that's up to them," he added.
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Labour leadership candidate Liz Kendall has said she intends to vote in favour of the Assisted Dying Bill.
Kendall told LBC radio that she believed the right safeguards - diagnosis of a terminal illness, certification from two doctors and judicial oversight - for the bill to be taken forward.
I believe in giving people as much power and control over what happens to them as possible.
People need the ability to die in their own homes. I believe this will be a step forward.
The Assisted Dying Bill, drafted by Lord Falcanor is due to be debated in the House of Commons on September 11.
Andy Burnham has warned fellow Labour MPs that the party must "pull together" in the event of a Jeremy Corbyn victory - despite many saying they would refuse to work under the left-wing leadership frontrunner.
Burnham, who is also a challenger in the contest, indicated he would be willing to feature in a Corbyn shadow cabinet, stating: "I will serve the Labour Party in whatever capacity I can".
The former health secretary said: "Coming out of this contest I believe there is an onus on all of the candidates, everyone in the party actually, to pull together and keep Labour as a united party.
"We must not go back to those days when we were fighting each other. There is no surer way to make yourself irrelevant to the country [than] if you are more interested in internal bickering than taking the fight to the government."
Teams backing Burnham and rival Yvette Cooper both urged each of the other's candidates to stand down from the race the previous day.
However, Cooper told ITV News Political Correspondent Libby Wiener that she was "in it to win it" and wanted to offer a "really strong alternative" to the Conservatives.
Neil Kinnock is the latest Labour heavyweight to warn the party over electing Jeremy Corbyn as leader.
Lord Kinnock, who lost two elections to the Conservatives, said he understood why people were supporting the left winger but the party had to make a decision about contesting power.
"I can see why people are angry and want to protest," he said.
"But then they have got to make a decision whether they want to be part of a Labour movement which produced a political party to seriously contest democratic power or they want to be in perpetual demonstration, which is fulfilling and noble but ultimately rarely effective."
Jeremy Corbyn dismissed suggestions that he should withdraw from the leadership race for the good of the party.
Responding to earlier criticism from David Miliband, he told ITV News' Political Correspondent Lewis Vaughan Jones:
"Miliband lives in New York and may be unaware of the excitement that the leadership contest has aroused in Britain."
He also reacted angrily to suggestions that the 600,000 registered voters were unrepresentative of the country as a whole.
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Yvette Cooper and Liz Kendall have denied reports that Lord Mandelson tried to persuade the three mainstream Labour leadership candidates to quit the leadership contest and force the party to stop the election.
The move by the former politician and 1997 election campaign leader highlights maneuvers within the party to stop Mr Corbyn winning the election.
Ms Cooper said she had not been approached directly by the Labour peer, she was unaware if her campaign team had been contacted.
I’ve not discussed this with Peter Mandelson.
I gather there was some view that maybe the whole process should be stopped because so many people were joining at the last minute. I don’t think that’s right.
I think it’s a good thing that people are joining the party.
Ms Kendall insisted that neither she nor her office had spoken to him.
Jeremy Corbyn has addressed a huge crowd of supporters outside Ealing Town Hall who could not get into the packed rally inside.
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