Ash Regan and Kate Forbes write open letter demanding for SNP membership numbers to be published
The SNP's national executive committee will hold an emergency meeting on Thursday morning amid a row over transparency, Sky News understands.
It is likely this could lead to the membership figures being released after the party refused to meet demands from all three candidates vying to replace Nicola Sturgeon as Scotland's first minister to publish the number of eligible voters.
There has been widespread criticism of "secrecy" in the contest.
On Wednesday, Kate Forbes and Ash Regan joined calls from Humza Yousaf for greater transparency from Peter Murrell, the SNP's chief executive and the husband of Ms Sturgeon.
In an open letter to party chiefs, both Ms Regan and Finance Secretary Ms Forbes called for the SNP to reveal the number of paid-up party members, as well as the number of digital voting documents and postal voting papers issued
It comes as candidates have reportedly been advised that the number of votes, percentage share and turnout will be published at the conclusion of the election.
The letter states: "We request that you provide essential information pertaining to the current membership status and voting procedures within the SNP, which is necessary for ensuring a fair and transparent leadership election."
"We have previously reached out to the national secretary, Lorna Finn, with a request for this information.
"However, we have yet to receive a response, which has prompted us to address this matter through a formal open letter."
The team representing Mr Yousaf said they made similar representations on Tuesday.
Former community safety minister Ms Regan and Ms Forbes state it is Mr Murrell's responsibility to ensure the election process is "transparent, fair, and equitable".
They added: "Your cooperation in this matter will not only demonstrate the SNP's commitment to democratic values and principles but also help maintain a strong and united party during this leadership contest."
SNP debate: 'Sturgeon would have been watching through her fingers'
Does hunger for independence remain in Scotland's 'Yes' towns and cities?
In Full: Watch the SNP Leadership Debate
Independence and poll woes - key moments of fiery Sky News debate
The SNP has so far refused to confirm how many party members will be able to take part in the vote.
Figures from the Electoral Commission show that in December 2021, the SNP had around 104,000 members.
However, there are uncertainties over the exact size of the electorate after the Mail on Sunday reported that only 78,000 online forms were being sent out.
An SNP spokesperson said: "Candidates have already been made aware that responsibility for the leadership election does not rest with any member of staff."
Click to subscribe to the Sky News Daily wherever you get your podcasts
Voting in the SNP leadership election, which is using the single transferable vote system, opened on Monday with the winner to be announced on 27 March.