Intelligence led investigators to believe the Belgian suspect was in an apartment in Saint-Denis to the north of Paris, triggering a ferocious seven-hour shootout there with police that began before dawn.
Paris prosecutor Francois Molins said the raid had thwarted a "team of terrorists that... Could have struck".
At least two people were killed -- a woman thought to have blown herself up with a suicide vest and another body that was found riddled with bullets, the prosecutor said.
A series of explosions rang out as the police closed in on the dwelling and one suspect was seen being dragged away, his bare buttocks exposed.
At least two bodies were found in the badly damaged building after the shootout, but identifying them was proving difficult, Molins told a press conference.
The body that had sustained a number of gunshots was "not in a state that allows it to be identified", he said.
Due to the severe damage to the building, it was impossible to know how many died and who they were, the prosecutor said.
"A new team of terrorists was neutralised and all indications are that given their arms, their organisational structure and their determination, the commando could have struck," he said.
Eight people were arrested but neither Abaaoud nor 26-year-old Salah Abdeslam, suspected of taking part in the attacks in Paris with his suicide-bomber brother Brahim, were among those held, the prosecutor said.
Abaaoud is a 28-year-old Islamic State fighter who was previously thought to be in Syria after fleeing raids in his native Belgium earlier this year.
A key piece of the evidence in the investigation had been a mobile phone found in a bin near the Bataclan, where 89 people were killed in the worst of the violence.
Residents of the Paris suburb of Saint-Denis said they had been caught in a terrifying exchange of fire.
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