"Islamists will not sleep peacefully in France. Fear will switch sides," Macron said at the meeting, held late on Sunday.
According to BFMTV, starting Monday, checks will be conducted of the authors of 80 posts on social media that express support for the attacker.
On Friday night, a history teacher, later identified as Samuel Paty, 47, was attacked and decapitated by an 18-year-old refugee of Chechen origin. The attack came after Paty showed a caricature of the Islamic prophet Muhammad to his students at a school in Conflans-Sainte-Honorine, northwest of Paris.
The killer, identified as Abdullakh Anzorov, was shot dead by French police shortly after the attack.
According to French media reports, 11 people, including four members of the attacker’s family, have been detained as part of the ongoing investigation.
According to France’s anti-terrorism prosecutor Jean-Francois Ricard, the suspect was born in Moscow in 2002, was of Chechen origin, and had received refugee status in France.
Chechen leader Ramzan Kadyrov has condemned the attack on the French teacher, urging French investigators on Saturday not to seek a "Chechen trace" in the attack, and stressing that the attacker had spent most of his life and was likely radicalized in France.