The Russian army said earlier that security forces on Tuesday had killed Maskhadov, and Chechen police confirmed the dead body was his.
Russian television showed what it said was Maskhadov lying, bare-chested on his back in a pool of blood, with his arms spread out on either side. There was what appeared to be a bullet mark in his left cheek.
"A special operation was carried out by us in the village of Tolstoy-Yurt as a result of which the international terrorist and leader of the rebel group Aslan Maskhadov was killed," Patrushev told Putin.
Tolstoy-Yurt is 20km north of the Chechen capital, Grozny.
Four close associates of Maskhadov had been detained, Patrushev was shown on television telling Putin. He added that there had been no casualties among Russian security forces.
Russia's FSB security service said
it carried out the operation
Putin asked Patrushev to double-check the report of Maskhadov's death.
Aljazeera's Moscow correspondent, Akram Khuzam, quoted the Chechen official Ziyad al-Sabsabi as saying that Maskhadov had been killed.
The killing of Maskhadov was a result of a joint military operation involving Russian special forces, the security forces and pro-Moscow Chechen fighters, al-Sabsabi told the correspondent.
"I have no details of how the operation was conducted, but the Russians could have killed Maskhadov long ago had it not been for the tactics he used to follow by constantly moving from one location to another," the vice-president said.
Zakayev does not doubt Russia's
account of Maskhadov's death
In London Maskhadov's spokesman Akhmad Zakayev said his death was a great blow but would not stop their cause.
Zakayev said the separatists would name a successor to Maskhadov within days, but he gave no hint as to who that would be.
Earlier Zakayev confirmed Maskhadov's death. "It's definitely Maskhadov," he said.
But Mashkadov's envoy to the Nordic countries, Usman Ferzaouli, who is based in Copenhagen, said: "They have confirmed it many times. They have confirmed that the war in Chechnya is over many times."
"If still we and my colleagues have not heard anything, then the president (Maskhadov) is not killed but alive," he said.
Maskhadov had a $10 million price on his head. Moscow blames him for a string of deadly operations in Russia, including an attack on a Moscow theatre, a bombing opposite the Kremlin, and an armed action against a school in the south Russian town of Beslan.
Maskhadov had denied involvement in the Beslan siege.
Recently, Maskhadov had called for talks with Moscow on Chechen demands for independence, but the Kremlin said it would not negotiate with "terrorists".
"If still we and my colleagues have not heard anything, then the president (Maskhadov) is not killed but alive"
Maskhadov envoy to Nordic countries
Some critics of Moscow's policies in Chechnya saw Maskhadov as a moderate with whom the Kremlin could negotiate.
Russian leaders, fearing a breakaway by Chechnya could trigger secession moves by other regions in the sprawling federation, have fought two wars in Chechnya.
Tens of thousands were killed on both sides in the first conflict from 1994-96.
Putin sent troops back into the territory in 1999 to cement his image as a strong leader before his election as president in 2000. The territory suffered widespread devastation and thousands more were killed.