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.
Mr 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 France at the weekend to honour him and defend freedom of speech. A silent march was held on Tuesday evening in the suburb north-west of Paris where he was killed.
A man named as 18-year-old Abdoulakh A was shot dead by police after killing Mr Paty on Friday.
The father of the pupil is reported to have exchanged a number of text messages with Mr Paty's killer prior to the attack close to the teacher's school in Conflans-Sainte-Honorine.
He is accused, along with a preacher described by French media as a radical Islamist, of calling for Mr 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 had been arrested and were being investigated for an "assassination in connection with a terrorist enterprise".
Police launched a series of raids targeting Islamist networks on Monday, and some 40 homes were targeted.
On Tuesday, French President Emmanuel Macron said the Sheikh Yassin Collective - an Islamist group named after the founder of the Palestinian militant group Hamas - would be outlawed for being "directly involved" in the killing.
He said the ban was a way of helping France's Muslim community, Europe's largest, from the influence of radicalism.
The group's leader is among 16 people who were taken into custody in the aftermath of the murder.
Six have now been released after questioning including the killer's grandfather, parents and 17-year-old brother. Four school students are believed to remain in detention.
Mr Darmanin earlier 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.
He said police would also be interviewing about 80 people who were believed to have posted messages in support of the killing.
Also on Tuesday, the French government ordered a mosque to close for sharing videos on Facebook calling for action against Mr Paty and sharing his school's address in the days before his death.
The Pantin mosque, which has about 1,500 worshippers and is situated 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.
A divided nation exposed
Beneath the public outrage there is a divided nation. A growing number of people believe France's rules on secularism and freedom of speech need to change.
Around 29% of Muslim respondents told a recent poll that Islam was incompatible with the values of the French Republic - a sharp increase over the past few years. And among those under 25, the figure was much higher.
The number of people who think violence is justified in response to cartoons of Muhammad is very small. But teachers in some areas say that view is growing among their pupils.
The roots of this rebellion against French national values are complex - conflicts abroad, racism, lack of opportunity and government policy all play a role.
It's hard to support the values of Liberty, Equality and Fraternity if they don't appear to apply to you.
Before this attack, President Macron had already promised a new law to target "separatism". But will it tackle the growing chasm or deepen the fault-lines once more?
Why was Samuel Paty targeted?
On Monday, anti-terrorism prosecutor Jean-François Ricard said Mr 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.
Mr Ricard said that the killer went to the school on Friday afternoon and asked students to point out the teacher. He then followed Mr Paty as he walked home from work and used a knife to attack him.
Tuesday evening's silent vigil in Conflans-Sainte-Honorine was attended by thousands. Earlier in the day, the French parliament observed a minute of silence.
Mr Macron will attend a ceremony with Mr 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% of the population.
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.