Accounts differ on how the Russian raid led to the rebel leader's death
But spokesmen for the leader, killed in a raid on Tuesday, said the struggle against Russian rule would continue.
It is unclear if the killing will boost Russia's grip in Chechnya, experts say.
Moscow had blamed Maskhadov for being involved in a string of deadly attacks, including the Beslan school siege. Maskhadov had denied the claims.
Maskhadov, who was elected president of Chechnya in 1997, was seen as the most moderate of Chechnya's rebel leaders, analysts say.
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The Chechen conflict
On Wednesday, radical Chechen leader Shamil Basayev - who claimed responsibility for the Beslan attack and also the theatre siege in Moscow in 2002 - vowed that the fight against Russia would go on.
"Mujahideen [fighters] come and go. Those who fought for Maskhadov can rest," a statement attributed to Mr Basayev and posted on the Chechen rebel Kavkaz Center website said.
"For those who fight for Allah, the jihad [holy war] continues," the statement said.
Mr Basayev - alongside with another field commander Doku Umarov - are seen as possible candidates to succeed Maskhadov.
A Russian military commander in Chechnya formally identified Maskhadov's body on Wednesday, the Itar-Tass news agency reported.
According to officials quoted by another Russian news agency, Interfax, the body would be buried in an unmarked grave rather than returned to relatives.
'Strategy beheaded'
Maskhadov was killed in a special operation by Russia's security services in the village of Tolstoy-Yurt near the regional capital, Grozny.
Accounts differ on how he died: the Russian military claims he was killed by a grenade flung into his underground bunker after he refused to surrender but a Chechen politician said he had been shot dead accidentally by one of his own bodyguards.
Vladimir Vasilyev, chairman of the security committee of the Russian parliament, or Duma, said the killing would put Chechen militants on the back foot.
"It creates a situation whereby it is not terrorist acts they are thinking about, but survival," he said.
Nataliya Narochnitskaya, from the Duma's committee of international affairs, told BBC News that the "terrorist strategy" in Chechnya had been "beheaded".
She dismissed suggestions that Maskhadov was a moderate who could have partnered Russia in negotiations.
"I don't know any case in the world history of terrorism that any political demands were ever the topic of negotiations with terrorists," she said.
The EU has urged Russia to work towards a peaceful solution to the Chechen conflict while respecting human rights.
Urging caution
An envoy for Maskhadov in London, Akhmed Zakayev, said earlier a successor would be chosen within days.
Unlike Maskhadov, both Shamil Basayev and Doku Umarov have been opposed to talks with the Kremlin.
The BBC's Sarah Rainsford says Moscow is celebrating a major coup but some others are urging caution.
Maskhadov, she says, was widely seen as someone Moscow could negotiate peace with if it chose.
After the recent killing of Chechen rebel leader , it was not clear who would take his place. His son Anzor Maskhadov, aged 29, has quickly emerged as the most likely candidate to carry on his father's work.

Speaking at his home in , Azerbaijan, Mr. Maskhadov told the Reuters news agency ''"I will continue my father's work. I have been in touch with his associates who are living abroad."'' He went on to describe the killing of his father as a ''"terrorist act"'' planned by the Russian authorities.

The Chechnya area of Russia has effectively been at war with Russia for much of the past decade: pro-independence guerrilla groups are faced by Russian regular army and special police forces. Numerous crimes against civilians and human rights infringement incidents reported in the area, involving both Russian army and rebel groups. 

Late President Maskhadov was considered a moderate pro-independence Chechen leader, in contrast with . He made numerous negotiations offers, all of them left unanswered by the . With Russian forces nominally controlling most of the Chechnya, his ability to control Chechen warlords was being questioned, though he reportedly managed to maintain lateral cease-fire in most parts of Chechnya shortly before his death. 

Maskhadov was the last publicly elected leader of the self-proclaimed Republic of Ichkeria. It's first elected president,  was killed in the sophisticated special forces operation of Russia's FSB in the 1990s.

Russian state run-media and MPs hailed the killing of Mr. Maskhadov — many believing his rebels were responsible for the  and the  in 2004.

Russian government took the hard-line position against Chechen rebels, denying any negotiations with the rebels after hostage takings and bomb explosions in Moscow (), downed airliners, hostage taking in  and other terrorist acts attributed to Chechen rebel groups. In many cases, Chechen groups claimed responsibility for these acts. Maskhadov denied any involvement in terrorist acts. According to Russian government's point of view, the war in Chechnya is merely a 'counter-terrorist operation' with an objective to 'restore the constitutional order'.