Algeria coach Djamel Belmadi made derogatory comments about the referee in a meeting with the GFF.
Belmadi appeared to encourage verbal and physical attacks on the official in a video posted by Algeria's football federation.
Algeria missed out on a place in the World Cup after they lost 1-2 to Cameroon in a World Cup qualification match on March 29th.
The verbal attacks against Gassama have caused grave concern for the GFF.
A statement from the organisation said it had made a formal complaint to the FAF and asked for investigations and proceedings against Belmadi.
The GFF asked the Algerian federation to make a public statement condemning the actions of Mr Belmadi and all the verbal attacks against Mr Gassama.
FAF should take all necessary precautions to prevent their officials and nationals from making any further negative remarks and threats against Mr Gassama.
They will be held responsible for any harm which may happen to him if they don't act.
At the past two World Cup and three matches at the Africa Cup of Nations, Gassama has been the referee.
The FAF requested that the play-off match against Cameroon be re-enacted due to the controversy surrounding it.
Algeria's Islam Slimani had two goals ruled out, one for offside and one for handball, before Karl Toko Ekambi scored the winner for the Indomitable Lions.
Belmadi said in a video posted on Sunday that they will never allow a few people to plot against the country.
I didn't like to see the referee sitting in the lounge suite with a coffee and a pastry the day after he left. I did not like that.
I didn't like the fact that we would accept these kinds of things. We treat him like this because he stole the hope of a whole nation.
I am not saying you have to kill him. He is more of a bully than a bully. We cannot accept that again.
Belmadi said that he told Gassama what he thought of him when he ran into him again in Turkey.
I told him who he was again, and then I told him who he was.
If they win, you are the good referee and if they lose, you are the bad referee, according to Gassama.
The president of the Federation of African Football said his organisation may contact the world governing body about the comments made by Belmadi.
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