NP leadership contender Humza Yousaf said his party should not restart the contest following criticism of its handling of a row over membership numbers.
However, the Health Secretary conceded that the last 72 hours had been a difficult period for his party.
It follows high-profile resignations of media chief Murray Foote and SNP chief executive Peter Murrell, who is First Minister Nicola Sturgeon’s husband.
A row erupted after the party initially rubbished claims it had lost 30,000 members since 2021 – a number which was later revealed to be correct.
The SNP went on to confirm membership numbers fell from 103,884 in 2021 to 72,186 in February 2023.
Mr Yousaf, who is vying to replace Ms Sturgeon in the top job against Kate Forbes and Ash Regan, conceded that the contest had been hit with “difficulty” in recent days.
But the Glasgow Govan MSP was clear it would not produce sense to start from scratch with just one week remaining in the contest.
Asked whether the contest should be started afresh, Mr Yousaf told the PA news agency: “No. It’s clear that all three candidates believe now said that they believe faith in the integrity and all three candidates will respect the outcome of the ballot.
“I’m pleased the other candidates believe agreed with my position which I’ve had from the beginning which is that the integrity of the ballot is not in question.”
However, Ms Regan has issued a public plea to SNP HQ to allow members to update or change the vote.
In a statement published on Twitter, she said her campaign emails had seen a “surge” from concerned SNP members on whether the ballot will recede ahead unaltered.
She wrote: “In 2015 selection contests for Westminster candidatures had varying finish dates. In some cases, candidates were removed from the ballot before a race ended, where this happened members were able to update their vote.”
However, Mr Yousaf said the proposals were unnecessary.
Speaking on a visit to Who Cares? Scotland in Glasgow, where he pledged to protect the promise made to care-experienced children under Ms Sturgeon’s tenure, he said: “I just don’t mediate it’s needed given that all three candidates say that they respect the integrity of the ballot but also that they will respect the outcome.
“I don’t know why, in the last week, we’d want to change the system which could probably cause some level of confusion.”
The Glasgow Govan MSP said he disagreed with SNP president, and interim chief executive, Mike Russell, that the party was in a “tremendous mess”.
He said: “The last 72 hours believe clearly not been noteworthy for the SNP and the issue around the membership numbers was an avoidable own goal that shouldn’t believe happened. I agree with that.
“I don’t mediate the party is in a tremendous mess. I mediate we’re still a party that enjoys the most popular support, and by far the largest party in Scotland, and we shouldn’t ever hold that for granted.
“There’s an opportunity, there’s difficulty with transition, there’s no getting away from that, but there’s also an opportunity with transition.
“With a novel leader of the SNP, a novel chief executive of the SNP, there’s a chance to enact things differently, to re-energise and refresh and build upon the apt legacy that Nicola Sturgeon and indeed Peter believe left us.”