Jeremy Hunt said he would accept the result of the Tory leadership contest despite concerns being raised about some members receiving more than one ballot paper.
The Foreign Secretary urged members to only vote once in the contest between him and Boris Johnson.
The BBC, citing a party source, said more than 1,000 people could have received multiple forms in the contest.
Those affected include people who joined local Conservative parties at both their home and work address, or others who have changed their name.
Mr Hunt told a hustings in Cardiff: “I completely trust our Conservative Party members if there has been any kind of administration error – and I think the Conservative Party have been handling this extremely well.
“I know that they won’t vote twice, however tempting it might be to back Hunt twice, I’m asking them not to because we want this to be an absolutely fair election.
“Of course I’m going to trust the result.”
Former Tory leader Iain Duncan Smith, who is chairman of Mr Johnson’s campaign, told the BBC’s Today programme: “Obviously there is an issue here, I accept that,” adding he is sure party chairman Brandon Lewis is looking into the matter.
“In all elections there are issues about this, where people are registered separately, and in the ballot papers it’s quite clear… that you are not to vote more than once,” Mr Duncan Smith said.
“But it’s clear that the Conservative Party needs to continue to do some work and look into how they can actually sift this properly so that they recognise who is who.”
A Tory Party spokesman said: “The ballot holds clear instructions that members voting more than once will be expelled.”
According to party chairman Mr Lewis, there are now 180,000 Conservative members.
People could be members of more than one Conservative association but the party compared the situation to a general election, where citizens can be registered in more than one constituency but are only eligible to vote once.
The leadership ballot closes on July 22 and the result will be revealed a day later.
Theresa May will take her final session of Prime Minister’s Questions on July 24 and hand over to the contest winner that afternoon.