"The Leader of the Revolution, Chairman of the African Union, will work to repair the situation that relations between the two brotherly countries Egypt and Algeria were subjected to..." it said.
Libya has borders with both Algeria and Egypt.
The troubles began when the Algerian team bus was attacked with stones before a group-stage match on November 14, injuring three players.
Egypt won the game 2-0, forcing the play-off in Khartoum, Sudan's capital. In the days after the first game, mobs in Algeria ransacked the offices of Egyptian companies.
After the second match in Khartoum, Egyptian newspapers unleashed stirring headlines about Egyptian fans being attacked by machete-wielding crowds.
Sudanese police said there were only a handful of injuries.
"Barbaric attacks on Egyptian fans in Khartoum," read one headline in the Egyptian daily Al-Masry Al-Youm.
"Algerians chase Egyptian fans with knives and machetes," said another.
Cairo withdrew its ambassador to Algiers last week and Algeria has demanded an explanation from Cairo.
Hosni Mubarak, Egypt's president, said on Saturday that Egypt would not allow its citizens abroad to be humiliated.
Ibrahim Youssri, a former Egyptian ambassador to Algeria, told Al Jazeera that the introduction of Gaddafi as a mediator would "give the leaders a chance to save face".
"But I do not think it will happen in a short time, maybe in a few weeks.
"But things are calming down. People in the two countries are very sad about this. The Egyptian and Algerian intellectuals wrote and spoke against all of these developments which have not reason or logic at all."