Merah, who killed seven people in three separate attacks, was buried in Toulouse on Thursday after being killed in a shoot-out with police on 22 March.
Police have been hunting possible accomplices but sources said there was no direct link with the raids.
Mr Sarkozy told Europe 1 radio after Friday's raids: "It's our duty to guarantee the security of the French people. We have no choice. It's absolutely indispensable."
Forsane Alizza The raids were carried out by the domestic intelligence agency, the DCRI, with the help of the elite Raid police commando group, Agence France-Presse news agency reports.
Several of the raids were in Toulouse, particularly the Mirail quarter, sources told AFP.
But there were also raids in Nantes, which is believed to be a centre for the Forsane Alizza (Knights of Pride) group, to which Merah had been linked by some French media.
It is a Salafist group that was dissolved by the interior ministry in an earlier investigation.
One of those arrested was the group's suspected leader, Mohammed Achamlane.
Police sources told AFP that three Kalashnikovs, a Glock pistol and a grenade were seized at his home.
Other raids took place in Lyon, Marseille, Paris, Nice, Rouen and Le Mans.
The BBC's Christian Fraser in Paris says the DCRI had been criticised for allowing Merah to slip through the gaps, so the agency now appears to be concentrating on people that may have slipped from focus over the past few months.
Merah's brother, Abdelkader, has already been charged with aiding him and police are hunting a third man said to be involved in the theft of a scooter that Merah used in all the killings.
Police also say a USB memory stick that was posted to the al-Jazeera TV channel containing the video he took of the killings must have been posted by someone other than Merah.
'Profound trauma' After Merah's killings, President Sarkozy ordered police to evaluate the level of danger posed by those known to sympathise with radical Islamists.
Mr Sarkozy told Europe 1 on Friday that arrests of suspected radical Islamists "would continue and that will allow us to expel from our national territory a certain number of people who have no reason to be here".
- French citizen of Algerian extraction, aged 23
- Had criminal record in France for non-terrorist crimes
- Had described himself as an al-Qaeda member and has spent time in Afghanistan and Pakistan
An opinion poll late on Wednesday suggested Mr Sarkozy was now ahead of main challenger Francois Hollande in first-round voting intentions - by 30% to 26% - and had narrowed Mr Hollande's lead in the largely expected run-off vote on 6 May.
Merah, 23, was buried at the Cornebarrieu cemetery in Toulouse on Thursday. His body was accompanied by around 15 men, although it was not clear who they were.
Toulouse's mayor had said it was "inappropriate" for Merah to be buried there, but Algeria, where his family is originally from, had refused to accept his body.
Merah died in a police assault on his flat in Toulouse on 22 March after a 32-hour siege. He had killed three soldiers in two separate attacks before shooting dead three children and a teacher at a Jewish school.
Merah is said to have told police he wanted to avenge Palestinian children and to attack the French army because of its foreign interventions.