LE PECQ, France — Police in France questioned four 10-year-olds who voiced support for the beheading of a schoolteacher and who said they would kill their own teacher if he lampooned Islam’s founder, the government reported as the prime minister warned Saturday that Islamic extremists are recruiting in France with “ignorance and hate.”

The children and their parents were detained and questioned for several hours Thursday by police in the Alpine town of Albertville, Interior Ministry spokeswoman Camille Chaize said.

On Monday, when French schools held a nationwide minute of silence to honor the slain teacher, Samuel Paty, the children voiced support for his killing last month near Paris, the spokeswoman said in a video statement Friday night.

They “justified the teacher’s assassination by arguing that it was forbidden to offend the prophet and adding that they would kill their teacher if he caricatured the prophet,” she said.

Paty was killed Oct. 16 outside his Paris-region school by an 18-year-old refugee of Chechen origin after he showed his class caricatures of Muhammad for a debate on free expression.

The children in Albertville were released after questioning. Judicial authorities ordered educative training for them, the ministry spokeswoman said. Police also searched their homes.

Paty’s killing was followed Oct. 29 by the killing of three people in a knife attack at a church in Nice. Leading a Saturday memorial for the victims in the Mediterranean city, French Prime Minister Jean Castex warned that extremists were recruiting French citizens.

“We know the enemy,” Castex said. “Not only is it identified, but it also has a name: It is radical Islamism, a political ideology that disfigures the Muslim religion by distorting its texts, its dogmas and its commandments to impose its dominance by ignorance and hate, an enemy that benefits from support overseas but, alas, also counts French citizens in its ranks.”

A choir sang “What a Wonderful World,” famously recorded by Louis Armstrong, and soldiers stood in silent ranks to honor the victims — Nadine Devillers, Simone Barreto Silva and Vincent Loques.

The chief suspect, Ibrahim Issaoui, a 21-year-old Tunisian, is in a French hospital after being wounded by police as they arrested him.

Paty’s killer was shot dead by police.

Meanwhile, authorities in France’s southeastern city of Lyon on Saturday ruled out a terrorism motive in the Oct. 31 shooting there of a Greek Orthodox priest, as they announced that a suspected gunman was in custody for the attack that critically wounded the clergyman.

The Lyon prosecutor’s office said the detained suspect is a 40-year-old man whose wife was having an affair with the priest. It said the man confessed to the shooting during police questioning.

The priest was shot twice in the abdomen with a hunting rifle as he was closing his church.