The 24-year-old Frenchman from Toulouse has said he belongs to al-Qaeda and acted to “avenge Palestinian children”.
Police are now negotiating with the man, who is still said to be heavily armed but has indicated he may give himself up in the afternoon.
Two police officers were injured in exchanges of fire during the raid and there are reports of a fresh blast.
The suspect’s brother is under arrest.
The suspect’s mother, who is Algerian, has been brought to the scene, but Interior Minister Claude Gueant, who is in attendance, said she had refused to become involved as “she had little influence on him”.
The minister said the suspect had made several visits to Afghanistan and Pakistan.
“He claims to be a mujahideen and to belong to al-Qaeda,” Claude Gueant said.
“He wanted revenge for the Palestinian children and he also wanted to take revenge on the French army because of its foreign interventions.”
The man shot at the door after police arrived, Claude Gueant said, injuring one officer in the knee and “lightly injuring” another.
The man has thrown one gun, a Colt 45, from a window, Claude Gueant said, but it is believed he has other weapons.
The minister said: “Our main concern is to catch him and to catch him under such conditions that he can be brought to justice.”
French media have linked the suspect to a group called Forsane Alizza (Knights of Pride) that was banned by Claude Gueant in January.
They also say the suspect had earlier been arrested in Kandahar, Afghanistan, for unspecified, but not terrorist-related, criminal acts and also has a criminal record in France.
Investigators report the suspect’s first name as Mohamed and that he was identified because of an e-mail message sent to his first victim about buying a scooter.
The message, sent from the suspect’s brother’s account, set up an appointment at which the soldier was killed, sources told AFP.
The man had also sought out a garage in Toulouse to have his Yamaha scooter repainted after the first two attacks. A scooter was used in all the attacks.
The house in Toulouse is a five-storey block of flats and the man is on the ground or first floor.
Police wearing helmets and flak jackets have cordoned off the area and prosecutors say other operations are under way to track down possible accomplices.
The brother was reportedly arrested in another part of Toulouse and a second brother has attended a police station, French media say.
The funerals of the rabbi and three children killed on Monday are under way in Jerusalem.
Israeli police said they expected thousands of people to attend.
The attacker gunned down Jonathan Sandler, a 30-year-old rabbi and teacher of religion, his two young sons Arieh and Gabriel and then – at point blank range – the head teacher’s daughter, 7-year-old Myriam Monsonego, in Monday’s attack at a Jewish school in Toulouse.
Their bodies were carried out of Ozar Hatorah school on Tuesday in two black hearses and taken to a nearby airport.
A military jet then flew them to Paris, from where they were placed on a commercial flight to Tel Aviv.
French Foreign Minister Alain Juppe has accompanied the relatives of the dead to the funerals in Jerusalem.
Also on Wednesday, French President Nicolas Sarkozy is to attend a memorial service for the three soldiers killed in the two attacks last week.
All three were of North African descent. Another soldier from the French overseas region of Guadeloupe was left critically ill.
Socialist presidential candidate Francois Hollande and Marine Le Pen, the leader of the far-right Front National, will attend the memorial service in Montauban.
After Wednesday’s raid took place, Marine Le Pen said the “fundamentalist threat has been underestimated” in France.
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