Labour officials are “rigorously, robustly and fairly” verifying that those applying to vote in its leadership contest do support the party, its interim leader says.
Harriet Harman said infiltrators were “not clever” but the party’s safeguards would ensure the “result will stand”.
BBC News understands 3,000 applications have been rejected. But there have been claims some are being blocked unfairly.
Labour peer Lord McConnell said the situation was a “shambles”.
Andy Burnham earlier warned “several thousand” Tories might have registered.
Mr Burnham, Jeremy Corbyn, Yvette Cooper and Liz Kendall are standing for leader.
More than 120,000 people have signed up to vote, along with more than 189,000 members of unions and other affiliates, bringing the electorate to more than 600,000.
New regulations allow members of the public to sign up to vote as a “registered supporter” for £3.
Mrs Harman told the BBC: “Because this is the first time we have operated these new rules for electing a Labour leader we have acted constantly on legal advice…
“I am absolutely certain that no court would decide that we had done anything other than apply the rules in a rigorous, fair, robust and even-handed way. So whoever is elected they will be legally elected.”
Mrs Harman said some Tory supporters were aiming to get a vote.
“That is dishonest and that is shameful for people who purportedly believe in democracy and support democracy,” she said.
Michael Dugher, Mr Burnham’s campaign chairman, suggested not enough was being done to address the issue of infiltrators.
Mr Burnham’s team have written to Labour’s general secretary claiming “a Conservative MP, Conservative media commentators, and Conservative councillors” had all been rejected.
Ms Cooper said the party should make sure processes are “robust”, but she wanted as many people as possible to take part.
A spokesman for Mr Corbyn, who polls suggest is the frontrunner, said he had confidence in the management of the election.
Speaking on BBC Radio 4’s Any Questions, Mr Corbyn rejected the suggestion it had been a “summer of blood” for Labour and said the campaign had been “good for democracy and for the party”.
He added it had been “absolutely fascinating” to attend hustings that were “ram-packed to overflowing” and to see “lots of young people joining for the first time and older people coming back”.
But Labour’s former First Minister of Scotland, Lord McConnell, described the situation as a “shambles” and said it had been a mistake to allow people to continue to register to vote in the contest throughout the summer.
He said there was a danger the issue would “overshadow” the latter stages of the leadership campaign, which he said should be about the “the vision” the candidates have “for the party and the country”.
He said: “This is a ridiculous situation and I cannot believe that when the initial decision was made in May to open up the membership in this way over the summer that somebody at a higher level in the party, or somebody in one of the at that time three main campaigns didn’t express some concerns.
“It seems I think in many ways to encapsulate what’s wrong with the running of the Labour party over recent years and why we’re in this mess in the first place.”
Responding to suggestions Mr Burnham or Ms Cooper could appeal against the result of the vote, Lord McConnell said he would be “amazed” if the contest had not been legally checked and said it unlikely it would be run again.
Labour says all applications to join as a full member, affiliate, or a supporter are assessed by a verification team.
The party says it has 40 staff in Newcastle and 30 at its London HQ working to check applications and anyone who does not support Labour’s “aims and values”, anyone not registered as an elector at the address they have given or anyone previously excluded from the party would be rejected.
MPs, local constituency parties and regional offices are also carrying out checks and providing further information. Applicants’ social media accounts are also being looked at.
Labour leadership contest
- Who are the candidates? Andy Burnham, Yvette Cooper, Jeremy Corbyn, Liz Kendall
- Dates: Ballot papers were sent out on 14 August; voting can take place by post or online. They must be returned by 10 September. The result is announced on 12 September
- Who can vote? All party members, registered supporters and affiliated supporters – including those joining via a union. More than 160,000 people signed up to vote as supporters, full members or union affiliates in the final days before the registration deadline, bringing the total size of the electorate to 610,000
- What is the voting system? The Alternative Vote system is being used, with voters asked to rank candidates in order of preference
- How does it work? If no candidate wins outright with more than 50% of first preferences, whoever is in fourth place drops out and the second preferences of their backers are reallocated to the other candidates. If there is still no winner the third placed candidate is then eliminated with their second preferences similarly reallocated. The candidate who has accumulated the most votes through the different rounds then wins.