"It does not rise to the level of a clear apology and, based on this, we're calling on the pope of the Vatican to issue a clear apology that will decisively end any confusion," Mohammed Habib, the deputy leader of the group, told Reuters.
Habib had earlier described the pope's remarks as a "sufficient apology".
The pope said he was "deeply sorry" at the anger caused by his remarks on Islam in a speech last week and said a quote he used from a medieval text about holy wars did not reflect his personal thoughts.
The pope had referred to criticism of the Prophet Muhamad by 14th century Byzantine Emperor Manuel II Palaeologus.
Habib said: "Why did he choose it (the quote) if it did not express his opinions? ... And if it does not express his thoughts and opinions, then let him tell us what his thoughts and perspective on this issue are."
The pope's remarks triggered angry street protests across the Muslim world.