Jennifer Stewart replaced Alan Donnelly after he was found guilty of kissing and touching a man at a civic function last year.
Mr Donnelly was ordered to pay £800 in compensation and will be supervised by the council's social work department for eight months.
Ms Stewart, a former Liberal Democrat who now sits as an independent in the ruling administration at Aberdeen City Council, told the BBC'd Good Morning Scotland programme that Mr
Donnelly would face a "witch hunt" if he continued to represent the Torry and Ferryhill ward.
"My concern is that if he does stay on - what I see - is that there is a bit of a witch hunt to get him out."
She added: "I have suffered at the wrath for three years of what the SNP and the Liberal Democrats have been like at Aberdeen City Council and I know how they will go on their witch hunt as they did with me.
"That's what I see is going to happen to Alan. Whether he chooses to remain is his decision - but if they make his life so intolerable and uncomfortable it might be that he chooses to step aside."
He added: "The people of Aberdeen, the people of Scotland will think that is the right thing that should be happening - he should be resigning and leaving office now."
The councillor claimed that the ruling administration was looking to ensure they kept control of the council, something Ms Stewart strongly denied.
He said: "In this case, your listeners will feel this is very much a stunt and is an attempt by the administration to maintain their control of Aberdeen City Council using a person who I don't think the people of Aberdeen think should be in office."
Stephen Flynn, SNP MP for Aberdeen South and Mr Nicoll's predecessor, said on Twitter: "A convicted sex offender should not hold public office.
"Genuinely stunned to hear the comments of the current Depute Provost of Aberdeen City Council this morning - defending the indefensible."