Merah had been under surveillance by French intelligence for years, Interior Minister Claude Gueant said.
The French defense ministry said Merah had twice tried to join the French military.
Merah was born in Toulouse, said Elisabeth Allanic, a magistrate at the Paris prosecutors office.
Late Thursday, his older brother, Abdelkader Merah, and their mother were still in police custody.
Mr. Merah was found dead on the ground, a bullet in the head, prosecutors said.
But at the same time Merah did not fit any "conventional" profile of a jihadist-to-be.
Prosecutors initially said Mr. Merah was 24 years old but later amended his age, to 23.
The French defense ministry said Merah had twice tried to join the country's armed forces.
Merah's brother Abdelkader has already been charged with helping him steal the powerful Yamaha scooter.
Cellphone numbers for the older Mr. Merah and his mother appeared to be disconnected.
Merah was sentenced 15 times by a Toulouse juvenile court when he was a minor, Molins said.
Merah said he had posted the video online, but police do not yet know where, Molins said.
Gueant said in Toulouse on Wednesday that he expected Merah to give himself up, but the standoff continued.
Aicha claimed that Mohammed Merah had beaten up her daughter, 19 at the time, and had threatened her.
From mid-August to mid-October 2011, Mr. Merah traveled to Pakistan, according to prosecutors.
French intelligence had been monitoring Merah as a suspected Islamist militant following trips he made to Pakistan and Afghanistan.
Mr. Merah had a long police record, with 15 arrests during his youth for petty crimes, French officials said.
Later in 2010, Mr. Merah made another bid to join the army, this time applying to the Foreign Legion.
He said Merah had been "polite and courteous" and had shown no signs then of a tendency toward radicalization.
As far as is known, Merah made no reference to any central Asian group during his standoff with authorities.
Police said they determined Mr. Merah's whereabouts Tuesday and moved to apprehend him in the early hours of Wednesday morning.
Merah also was opposed to France's recent move to ban women from wearing a full veil, or burqa, Molins said.
Mr. Merah appears to have been on the radar of French officials before the first killing now attributed to him.
Molins said the investigation into Forsane Alizza began in October 2011, and the arrests were not connected to Merah's rampage.
Police also questioned Mohammed Merah's mother and his brother Abdelkader's girlfriend, but have released them without charge, the Paris prosecutor said.
American officials in Afghanistan believe Mr. Merah was picked up by Kandahar police on one of his visits, U.S. military officials said.
After the incident, Mr. Merah was added to a U.S. no-fly list.
France's president has led tributes to the victims of Islamist gunman Mohamed Merah, who murdered seven people in Toulouse a year ago.
Mr. Merah was brought before a judge for the first time at age 16, for allegedly throwing a stone at a bus.
Etelin told BFM-TV he had represented Merah since 2004 or 2005, when his client was a minor, mostly over accusations of theft.
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