"If this person were really someone reasonable, he would not agree to remain at his post one minute, but would convert to Islam immediately," Mohammed Gaddafi told an awards ceremony on Monday evening for an international competition to memorise the Qur'an.
"We say to the pope - whether you apologise or not is irrelevant, as apologies make no difference to us."
Gaddafi junior also hit out at "those Muslims who look for comfort in the words of a non-Muslim".
He said Muslims "should not look for charity from the infidel... but should fight Islam's enemies who attack the faith and the Prophet Muhammad".
On Sunday, the pope said he was "deeply sorry" for the reaction to a speech he made last week in which he quoted an obscure medieval text that criticised some teachings of the Prophet Muhammad as "evil and inhuman".
The speech sparked several days of protests in Muslim countries against the leader of the world's 1.1 billion Roman Catholics.
Although the pontiff's apology was widely rejected as insufficient, anti-pope protests seemed to subside on Tuesday with the only planned event a rally by foreign theology students in the Iranian clerical capital of Qom.