Anti-terrorism prosecutor Jean-Francois Ricard said officials found a photograph of the teacher's body and a text claiming responsibility for carrying out the killing on the suspect's phone.
Five more people have been detained over the murder on Friday outside Paris, including the parents of a child at the school where the teacher was working, bringing to nine the total number now under arrest, said the source, who asked not to be named.
The history teacher's recent class discussion on freedom of expression, during which he showed his students cartoons of Prophet Muhammad, had prompted complaints from some parents.
The thread contained a video of a man who said his Muslim daughter was one of the pupils in the class - and she had been shocked by the teacher's actions.
Last month, a young man from Pakistan was arrested after attacking two people with a meat cleaver outside the former offices of the satirical newspaper Charlie Hebdo. Authorities say the attacker was later shot dead by police after he didn't respond to commands to disarm and acted threateningly.
Four relatives of the attacker, including a minor, were detained in the immediate aftermath of the attack in the middle-class suburb of Conflans-Sainte-Honorine.
The next day, the father went to see the principal of the school to complain, prosecutors said.
Police shot dead the 18-year-old attacker, who was born in Russian Federation, minutes after he murdered 47-year-old history teacher Samuel Paty in broad daylight in Conflans-Sainte-Honorine on Friday.
French President Emmanuel Macron, flanked by French Interior Minister Gerald Darmanin, speaks to the press following a stabbing attack in the Conflans-Sainte-Honorine suburb of Paris, France, Oct 16, 2020.
The suspected attacker was reportedly an 18-year-old man of Chechen origin and was unknown to police for radicalization.
Prosecutors said they were treating the incident as "a murder linked to a terrorist organisation" and related to a "criminal association with terrorists".
An arrest warrant is out for the father's half-sister, who has joined Daesh in Syria, Richard added.
The investigation will also look at a tweet from an account opened by the attacker, and since shut down, that showed a picture of Paty's head and described Macron as "the leader of the infidels".
His office said a national tribute would be held in Paty's honor.
Some carried placards stating: "I am a teacher" and "I am Samuel" - echoing the "I am Charlie" cry that traveled around the world after the 2015 Charlie Hebdo killings.
Addressing the country's teachers, pupils and their parents, Education Minister Jean-Michel Blanquer said Mr Paty was killed by what he called the enemies of freedom.
A parent of one of Paty's students told France's AFP news agency that, according to his son, the teacher had told Muslim students to leave the classroom ahead of the lesson and that he "didn't want to hurt their feelings".
Local centre-right lawmaker Antoine Savignat said, "If we can not talk about the Charlie Hebdo caricatures in school, we end up in denialism".