Molins praised the work of French investigators in identifying him in only four days.
Police have questioned other family members in Toulouse, including his mother, Zoulika Aziri, Molins said.
Mr. Molins described Alexandre as a troubled youth who converted to Islam just before he turned 18.
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.
Gibbs slotted England's sixth penalty but Molins' effort struck the outside of the post to give England victory.
At that time, he did not appear to represent any threat, Molins said.
Merah also was opposed to France's recent move to ban women from wearing a full veil, or burqa, Molins said.
Molins said the investigation into Forsane Alizza began in October 2011, and the arrests were not connected to Merah's rampage.
"We believe he is likely to have been the killer or one of the killers, " Paris prosecutor Francois Molins said.
When police arrived at his friend's house Wednesday morning, the suspect said: "I know why you are here, " according to Mr. Molins.
Molins, the prosecutor, said Tuesday the investigation into Forsane Alizza began in October 2011, and the arrests were not connected to Merah's rampage.
With 20 minutes remaining, Molins beat Kieran Gibbs down the right and his cross was slotted in by Berg from eight yards out.
Mr Molins said his fingerprints had been found on the remains of a grenade thrown into the kosher grocery store in the Paris suburb.
Mr Molins also said all three women were killed with one gun, adding that the reason for the murder had not yet been determined.
Footage then shows the suspect kneeling as if offering a Muslim prayer, eight minutes before allegedly stabbing Mr. Cordiez, the French soldier, Mr. Molins said.
He was sent back to France after Afghan police picked him up at a traffic stop and alerted international forces to his presence, Molins said.
Mr Molins also said that one of the detainees had acted as a contact for would-be jihadists while another had travelled to Egypt and Tunisia.
England paid the price for such profligacy as Sweden - galvanised by substitutes Labinot Harbuzi, Robin Soder and Molins - gradually chipped away at the deficit.
The suspect, who is being named only as "Alexandre, " will turn 22 on Thursday, Paris prosecutor Francois Molins said in a news conference broadcast by CNN affiliate BFMTV.
Alexandre was arrested outside the home of a friend close to Les Yvelines, near Paris, where he had been staying because he has no permanent address, Molins said.
Mr. Molins, who identified the suspect only by his first name, Alexandre, said police were able to track him down using video footage and DNA samples collected from the scene.
He had a prior record of petty crimes committed when he was under 18 and is known to have been rebellious in his youth, but was not known to French security services, Molins said.
Paris prosecutor Francois Molins described him as "a delinquent" and said his fingerprints had been found on the remains of a grenade thrown into the kosher grocery store in the Paris suburb of Sarcelles on 19 September.
Mr Molins, the Paris prosecutor, said the explosive ingredients found garage in the Paris suburb of Torcy on Tuesday night could have made "exactly the same kind of device as was used in 1995 by the GIA".
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