Andy Burnham has warned Labour MPs seeking to halt the party leadership contest they are making a "major mistake" and should allow the contest to focus on the issues if they want to prevent Jeremy Corbyn from winning.
Several critics have demanded a re-run after a rush of applications for a vote sparked claims the process was being undermined by political enemies on the right and left.
But Mr Burnham said that despite "appalling" behaviour by some individuals exploiting the move to open up the contest beyond party members and unions, and ongoing concerns about access to data, making that the centre of debate would backfire.
"The risk is if people make this about the process now, that will be to everyone's detriment. If it becomes an argument about the rules or an internal debate, that would be a major mistake," he told the Press Association.
"The important thing now is to keep it positive and focus on what each candidate is saying."
Despite concerns over "entryism", he defended the move - by Ed Miliband - to reform the rules.
"The idea was to open up politics and that's exactly what it's done, so you can't complain once the change has the effect you wanted to have," he said.
"So, this is not the time to cry foul on the rules.
"The process has engaged a lot of people. The other political parties couldn't manage anything like that number.
"Politics has become more and more remote from people in recent years. People do feel a sense of disengagement. This contest could mark a change."
He went on: "Some have signed up with negative intentions and they have been weeded out, and I would hope that they will continue to be weeded out.
"There are people who don't have the best interests of Labour at heart who have tried to influence this campaign.
"I think that is pretty appalling behaviour on their part, particularly Tory MPs and Tory-leaning journalists.
"But the processes are there. The party is going through an extensive process of checking."
His campaign team - along with those of Yvette Cooper and Liz Kendall - wrote to party chiefs over concerns they were being denied access to the contact details of a late rush of people signing up for a vote.
Mr Corbyn's team denied being given details by trade unions of new recruits from their ranks.
"We continue to challenge aspects of the contest. There was a large number of sign-ups yesterday and we need to know the implications of that in terms of whether we will have time to communicate with those people, find out who they are," he said.
"But that is all we are doing. We are clarifying; we are not challenging.
"My campaign is not crying foul in terms of the respect of the process or the rules. Yes, there are things to clarify here and there, but overall my focus is on those 600,000 voting members."
Mr Burnham said the campaign showed Labour was "ready for a big change in both the style and the substance of our politics", but that it had to be combined with economic "credibility" if it was to stand a chance of winning back power in 2020.
"It wants something substantial it can sell on the doorstep, it wants a vision that can excite and inspire, but also one that can win, and you can't win unless you have economic credibility, " he said.
"This is crunch moment now. I am putting my cards on the table. This is a bigger vision than any of the candidates have set out and I am confident that when the 600,000 voting members see my manifesto, I think I can persuade them."