Candidate Andy Burnham has said there is "no question" of any legal challenge to the contest.
He said Tuesday's meeting was "just to identify the processes to make sure" that Labour's opponents do not vote.
Ms Harman has said the party's rules are being applied in a robust and even-handed way.
Mr Burnham said it was necessary to ensure "that there are the right processes, that they're as thorough as they need to be and that we can identify the people who are trying to claim a vote on fraudulent grounds."
He said he had confidence in the process "as long as we get clarification about how the very small number of applications that have been made on a fraudulent basis [are] being dealt with properly".
The other candidates for the leadership are Yvette Cooper, Jeremy Corbyn and Liz Kendall.
There have been claims that opponents of Labour have registered as Labour supporters, giving them a vote.
There have also been complaints about some legitimate voters being unfairly excluded from voting.
Meanwhile, former deputy prime minister John Prescott says the contest could end up splitting the party.
Analysis
By Ross Hawkins, BBC political correspondent
Time after time, Labour officials have insisted that the leadership election is robust, and some involved in fighting the contest have made clear that they fear it could be deeply flawed.
They argue as Andy Burnham's campaign manager Michael Dugher did last week, that a failure now could lead to a legal challenge later.
Some insist data obtained when Labour teams canvassed voters during the election should be used to help weed out opponents of the party who have secured ballot papers, a proposal that so far has been rejected.
Others worry that valid voters could be deprived of a say by over-zealous officials.
But there is another concern - that a process designed to enthuse new supporters could see a debate about policies overshadowed by a bitter dispute about the conduct of this election.
Lord Prescott, speaking at a rally for Andy Burnham, compared former leadership contender Chuka Umunna and Tristram Hunt to the so-called "Gang of Four" MPs who left the party to form the SDP in 1981.
Mr Umunna and Mr Hunt have established the "Labour for the Common Good" group to look at how it can win back power.
Lord Prescott said their actions were making him "more than worried" that the party could be heading for a repeat of the 1981 split.
And ex-Labour cabinet minister Charles Clarke has described the leadership contest as a "disaster".
He told Newsnight the new voting rules brought in by former Labour leader Ed Miliband "were a mistake and many people argued that at the time".
Under new party rules, people have been able to pay £3 to become registered Labour supporters, making them eligible to vote.
All party members, registered supporters and affiliated supporters have a vote in the leadership election.
More than 160,000 people signed up to vote in the final days before the registration deadline, bringing the total size of the electorate to 610,000.
Source: http://www.bbc.com
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