SNP MSP for Aberdeen Central Kevin Stewart said allowing the councillors to re-join Scottish Labour would be akin to “jumping back into bed” with Boris Johnson.
The decision to continue the suspension of the councillors is not a decision for the leader, with the disciplinary process independent.
Mr Stewart said: “These disgraced councillors have worked hand in hand with the Tories for years now.
“Scottish Labour might talk a good game when it comes to fighting Westminster austerity, but the party won’t be taken seriously if they open the door for councillors who have propped up a right-wing Tory administration to re-join the party.
“If Monica Lennon and Anas Sarwar want to be seen as anything approaching credible candidates, then they must lead by example and make clear the suspension of these Tory supporting councillors will remain in place.
“Anything less is a clear admission that Scottish Labour are jumping back into bed with Boris Johnson’s Tories in a unionist pact.”
Mr Sarwar, who is the front-runner in the leadership contest, said that he does not consider the suspended councillors “ex-Labour”.
He said: “I don’t consider my colleagues to be ex-Labour councillors. To me, they are nine Labour councillors who are working day and night for the people of Aberdeen.
“Their determination to improve their local communities saw them named Local Authority of the Year.
“I look forward to working closely with them in the months and years ahead.”
Ms Lennon accused the SNP of “damaging our public services” and said she would “take no lectures from either of them”.
She said: “The SNP should get its own house in order. In government they have brutally cut council funding and hurt our communities.
“When it comes to damaging our public services, the Tories and the SNP have a lot in common. I’ll take no lectures from either of them.
“As Scottish Labour leader, I will expect all members to respect our rules and act responsibly. These disciplinary cases started two Scottish Labour leaders ago. The matter is closed and we must move on.”