Jeremy Corbyn says he only wants "genuine Labour supporters" to vote for him in the party's leadership contest.
It has been suggested that Conservative supporters and "hard left" activists have been registering for the vote in order to back the left wing MP.
As a result, two backbench MPs, Graham Stringer and John Mann, have called for the leadership contest to be halted.
But another leadership candidate, Andy Burnham, said he had seen no evidence of infiltration "on a large scale".
"If John [Mann] has evidence then he needs to send it to the Labour Party," he told Sky News.
Mr Mann told the Sunday Times the contest was "totally out of control", and said acting leader Harriet Harman should step in so proper checks could be conducted.
On BBC Radio 4's The World This Weekend, Mr Stringer called for the "deeply flawed system" - whereby non members can pay £3 to become an "affiliated supporter" and take part in the leadership election - to be scrapped.
"The party has a difficult choice. It either has to go ahead with this election or it has to delay the decision, or it has to change the system," he said.
Labour could end up with a leader "who is chosen by readers of the [Conservative-supporting] Daily Telegraph", he said, adding: "I am worried that people who do not have the interests of the Labour Party at heart are joining the Labour Party."
Labour says it has a "robust system to prevent fraudulent or malicious applications" and that anyone "not sharing the aims or values of the Labour Party will be denied a vote".
Speaking on the BBC's Andrew Marr Show, Mr Corbyn said: "I only want people to register as Labour supporters if they are genuine Labour supporters and they want to stay for the longer course."
Labour leadership contest
- Who are the candidates? Andy Burnham, Yvette Cooper, Jeremy Corbyn, Liz Kendall
- Dates: Ballot papers will be sent out on 14 August; voting can take place by post or online. They must be returned by 10 September. The result is on 12 September
- Who can vote? All party members, registered supporters and affiliated supporters - including those joining via a union
- What is the voting system? The Alternative Vote system is being used so voters are asked to rank candidates in order of preference
- How does it work? If no candidate gets 50% of all votes cast, the candidate in fourth place is eliminated. Their second preference votes are then redistributed among the remaining three. If there is still no winner, the third place candidate is eliminated with their second preferences (or third in the case of votes transferred from the fourth place candidates) redistributed. It is then a head-to-head between the last two candidates
The popularity of the Islington North MP's campaign has sparked a row within the party.
Former Prime Minister Tony Blair is among those to have warned Labour against moving to the left following a poll that put Mr Corbyn ahead of Andy Burnham, Yvette Cooper and Liz Kendall in the race to succeed Ed Miliband.
Mr Corbyn said he was "making no predictions" over the outcome but said he was in the contest "for real".
He also said it was not an "extreme position" to consider renationalising some privatised services, saying 60% of people backed returning the railways to public ownership.
He said he would be "much happier" with a "regulated, publicly run service delivering energy supplies".
Asked whether he saw himself as a Marxist, Mr Corbyn said it was a "very interesting question" and praised some of the revolutionary thinker's ideas.
He added he did not think party leaders should "lay down policies" and that instead they should "encourage the growth of ideas".
Ms Kendall, who has rejected suggestions she should quit to allow another candidate to defeat Mr Corbyn, told the Independent on Sunday Mr Corbyn's politics were "not right for Labour or the country".
In the Sunday Mirror, Ms Cooper said the party needed to "get serious".
"Get this wrong, and we will write off the 2020 election and condemn Britain to a Tory future," she added.
Former cabinet minister Alan Milburn told Sky News Labour risked being cast into "political oblivion", saying Mr Corbyn was a "perfectly nice chap - but I don't think even Jeremy thinks he is prime ministerial material".
Ex-SNP leader Alex Salmond said he could work with Labour on "a range of issues" if Mr Corbyn became leader.
Mr Salmond said the Islington North MP was a "substantial politician" and criticised his "demonisation" in the press, saying the two parties could co-operate on welfare reform and Trident renewal.