The father of a pupil accused of launching an online campaign against Samuel Paty, the teacher beheaded in France, sent messages to the killer before the attack, French media report.
Samuel Paty, who was killed on Friday, had earlier shown controversial cartoons of the Prophet Muhammad to his pupils.
The 48-year-old father, who has not been officially named, is accused of issuing a "fatwa" against the teacher.
The brutal murder of Mr Paty, 47, has shocked France.
Tens of thousands of people took part in rallies across the country on Sunday to honour him and defend freedom of speech.
A man named as 18-year-old Abdoulakh A was shot dead by police after killing Paty on Friday.
What's the latest?
The father of the pupil is reported to have exchanged a number of text messages with Paty's killer prior to the attack close to the teacher's school in Conflans-Sainte-Honorine, a north-western suburb of Paris.
He is accused, along with a preacher described by French media as a radical Islamist, of calling for Paty to be punished by issuing a so-called "fatwa" (considered a legal ruling by Islamic scholars).
Interior Minister Gérald Darmanin said the two men have been arrested and are being investigated for an "assassination in connection with a terrorist enterprise", French media report.
Police launched a series of raids targeting Islamist networks on Monday, and some 40 homes were targeted. More raids are expected and President Emmanuel Macron is due to chair a meeting on Tuesday to review the police operation.
Meanwhile, Darmanin said 51 French Muslim organisations, including charities and NGOs, would be inspected by government officials and closed down if they were found to be promoting hatred.
So far, a total of 16 people have been taken into custody in the aftermath of the murder.
The killer's grandfather, parents and 17-year-old brother were detained shortly after the gruesome attack. Four school students have been detained as well.
The interior minister also said police would be interviewing about 80 people who were believed to have posted messages in support of the killing.
On Tuesday, the French government ordered a mosque to close after it shared videos on Facebook calling for action against Paty and sharing his school's address.
The Pantin mosque, just north of Paris, will close for six months on Wednesday. The mosque expressed "regret" over the videos, which it has deleted, and condemned the teacher's killing.
Darmanin said the Pantin mosque, which has more than 1,500 worshippers and is situated in a busy suburb, shared the videos on its Facebook page just days before Paty's death on Friday.
Marlène Schiappa, French junior interior minister, met police chiefs on Monday to discuss the spread of radical material online. On Tuesday, she will meet the heads of social media networks in France to discuss so called "cyber-Islamism".
Why was Samuel Paty targeted?
On Monday, anti-terrorism prosecutor Jean-François Ricard said Paty had been the target of threats since he showed the cartoons of the Prophet Muhammad during a class about freedom of speech earlier in October.
The history and geography teacher advised Muslim students to leave the room if they thought they might be offended.
Ricard said that the killer went to the school on Friday afternoon and asked students to point out the teacher. He then followed Paty as he walked home from work and used a knife to attack him.
A silent rally is being planned for Tuesday evening and President Emmanuel Macron's office said he would attend a ceremony organised with Paty's family on Wednesday.
The teacher will also be posthumously given France's highest award, the Legion d'Honneur.
Depictions of the Prophet Muhammad can cause serious offence to Muslims because Islamic tradition explicitly forbids images of Muhammad and Allah (God).
The issue is particularly sensitive in France because of the decision by satirical magazine Charlie Hebdo to publish cartoons of the Prophet Muhammad. A trial is currently under way over the killing of 12 people by Islamist extremists at the magazine's offices in 2015 following their publication.
France's Muslim community comprises about 10 percent of the population, one of the largest Muslim minorities in Europe.
Some French Muslims say they are frequent targets of racism and discrimination because of their faith - an issue that has long caused tension in the country.
"In France, the vast majority of Muslims are of the republican philosophy," Education Minister Jean-Michel Blanquer told the BBC on Tuesday.
"We want them to be mobilised, as we want everyone to be mobilised to defend democracy," he added.
- BBC