"Hate preachers and propagandists of religious separatism should be prosecuted, and if they are foreigners, they should be expelled [from France] immediately," Le Pen said.
She added that each suspected Islamist radical assigned France's S card (Fiche S), which identifies him as a serious threat to national security, should be persecuted, and if he or she has dual nationality, must be deprived of French citizenship.
Le Pen said it was necessary to revise the country's migration policy "which feeds communitarianism - the soil for Islamists," advocating a moratorium on immigration and naturalization.
The politician has also called for setting up a commission of inquiry to establish why the deceased history teacher was "left unprotected by the state" in the face of the Islamist threat. Le Pen also proposed renaming some educational facilities after the murdered teacher.
French history teacher Samuel Paty was killed by beheading in the outskirts of Paris on Friday night. The main suspect for the murder, a Moscow-born 18-year-old teenager identified as Abdullakh Anzorov, was shot dead by security forces. The attack came after 47-year-old Paty showed a cartoon depicting Islamic prophet Muhammad to his students at the school in Conflans-Sainte-Honorine in a northwestern Paris suburb, outraging some Muslim parents.
French President Emmanuel Macron has denounced the attack, branding it as a terror act. At a Defense Council meeting on Sunday, the president ordered the implementation of widespread measures to combat Islamist extremism. The measures include tightening security in French schools to enter into effect after the fall break.
Meanwhile, the probe into the attack is underway, with 11 people currently in police custody, including members of the attacker's family.