In a series of tweets, Fani-Kayode claimed Alhassan, who is popularly known as Mama Taraba, was "intimidated" into changing her position.
He tweeted: "Mama Taraba should continue to stand on the platform of truth and not allow herself to be intimidated. I reacted to a story in which she allegedly exposed @elrufai.
"It took her 24 hours to deny the story and I wonder why.If the story is not true she should blame the original source, medium and author of the allegation and not me.
"I merely reacted to it like millions of other Nigerians did. She should clean up her stinking mess and not blame me for it.
"I guess that it is also not true that her associates in the APC government have alleged that N12m went missing under her watch as Minister and that she now supports @atiku against her own boss.
"She should stand firm and stop blowing hot and cold. U cannot serve God and the devil at the same time.
"I repeat she should clean up her stinking mess and understand that I am not a soft or easy target. Whichever way the APC sun is still setting.
"My advice to her is to stop getting her pretty knickers in a twist,to tow the path of honor, to resign from this accursed Govt. and to leave the APC before they strip her stark naked and feed her to the dogs."