Algiers-based lawyer Zahia Mokhtari told French media Mohamed Benalal Merah considered his son had been murdered.
Mr Merah's plan to sue the state drew criticism from French politicians.
"If I were the father of such a monster, I would shut my mouth in shame," French Foreign Minister Alain Juppe said on Tuesday.
'No al-Qaeda links' Ms Mokhtari told the AFP news agency that a convention signed between France and Algeria allows lawyers to pursue cases in both countries.
"Mr [Mohamed Benalal] Merah came to our office in Algiers yesterday [Tuesday] to formally ask us to sue the French security services for not having followed procedure during the attempt to arrest Mohamed Merah and his murder," Ms Mokhtari told AFP.
Mohamed Merah died in a police assault on his flat in Toulouse on 22 March after a 32-hour siege. He had killed three soldiers in two separate attacks before shooting dead three children and a teacher at a Jewish school.
Merah, born in France of Algerian descent, is said to have told police he wanted to avenge Palestinian children and to attack the French army because of its foreign interventions.
His half-brother in Algeria, Rachid Merah, said Mohamed had been manipulated by the French intelligence services and did not have any ties to al-Qaeda.
"I deny that formally and I have doubts that he had any link with al-Qaeda or Taliban or any terrorist organisation in the world. And the fact that proves it is that France killed him before he could speak in a trial, while they could get him alive," Rachid Merah said.
Merah's family want to bury him in Algeria but the Algerian authorities have not formally granted their request.