Dumfries and Galloway councillor Jim Dempster, who made an Islamophobic comment about Mr Yousaf, has said he is “deeply sorry” for the offence caused by his “totally unacceptable” remarks.
Cllr Dempster has been suspended from the Labour Party pending an investigation after making the comment.
He said the comments did not reflect the views he holds and he has asked to be given extra diversity training.
He has also visited a mosque and received support from a local imam as he bids to make amends.
Mr Yousaf renewed his call for Cllr Dempster to resign.
“After making such a blatant Islamophobic slur, a tokenistic photo-op at the local Mosque is frankly an insult,” Mr Yousaf tweeted.
“Cllr Dempster priority seems to be to try & save his political career.
“I once again call on him to do the honourable thing and resign.”
Cllr Dempster said, in a meeting with Transport Scotland officials a week ago, that if Mr Yousaf had visited the region “he may have been at Springholm, but no-one would have seen him under his burka”.
In a statement issued today, Cllr Dempster said: “I fully accept that my comments were totally unacceptable.
“I am deeply sorry for the offence I have caused and I offered a full and immediate apology.
“I do not believe that the comments I made reflect the actions or views that I have held during my service to my community.”
Cllr Dempster said he would accept the findings of the party’s investigation when it finished.
He went on: “I also had the honour of meeting with the imam at the mosque in Dumfries to seek his views.
“The imam has kindly invited me to address the mosque and work with members of the Muslim community.
“This will allow me to learn more about the issues facing ethnic minorities, especially in Dumfries and Galloway, and how the use of everyday language may affect them, and this will also give me the opportunity to reflect on and challenge and change my behaviour.
“I understand the hurt and offence such comments cause and have requested additional diversity and awareness training to be arranged for me.
“I cannot change the comments made, but I am committed to taking responsibility for my actions, and playing my part in challenging discrimination wherever it is displayed.”
Sardar Ahmad Rizvi, imam of the Islamic Centre in Dumfries, said in the joint statement: “I have met councillor Jim Dempster, who is a good man who has represented his community well for many years.
“I do not believe that councillor Dempster’s comments constitute racism, or believe he is a racist, but he understands the hurt they have caused and he has apologised.
“Our religion teaches the importance of forgiveness.”