Rebel figure Shamil Basayev said according to a 2002 agreement between Maskhadov and other Chechen leaders, former court chairman Abdul-Khalim Sadulayev was to succeed Maskhadov, the separatist website Kavkaz-Centre said.
Maskhadov's son Anzor said in an interview from his home in Baku, Azerbaijan, that Sadulayev's appointment would be formally announced on Thursday by Maskhadov's leading spokesman abroad, Umar Khambiyev.
The internet newspaper Gazeta.ru, citing Russian special services, said Sadulayev was the head of the separatists' Shariah committee and a Saudi national, one of five who came to the fore of the separatist movement in 2002 because of their ability to bring foreign funds to Chechnya.
But Anzor Maskhadov denied that, saying Sadulayev was Chechen.
Basayev praised Maskhadov's leadership. "Maskhadov was killed in a battle on the straight path to Allah, having travelled his portion in a worthy manner, showing all Muslims an example of a truly believing Muslim fighter, unexampled bravery, steadfastness, patience and strong faith," he was quoted as saying.
"Now a fierce and irreconcilable fight for this position will break out between so-called Ichkerians (separatist Chechens) who take shelter abroad and those who are still in the mountains"
Taus Dzhabrailov, chairman of the Chechen Council
Maskhadov was killed on Tuesday in a special operation by Russian security forces in northern Chechnya, leaving the fighters largely in the hands of Basayev, seen as the most hardline of the separatist leaders.
An official in the Kremlin-backed Chechen government predicted that a struggle would ensue for leadership.
"Now a fierce and irreconcilable fight for this position [of separatist leader] will break out between so-called Ichkerians (separatist Chechens), who take shelter abroad, and those who are still in the mountains," the Interfax news agency quoted Taus Dzhabrailov, chairman of the Chechen State Council, as saying.
The killing could undermine any chances of peace even as the Kremlin celebrates a politically valuable success in a conflict that has dragged on for more than a decade.
Even some supporters of the Kremlin's campaign seemed to doubt the killing would force an end to attacks - especially since Maskhadov, while a symbolic figure, was thought to directly control few of Chechnya's estimated 1500 separatist fighters.
"I don't think Maskhadov's death is such an irreplaceable loss for the rebels," Aslambek Aslakhanov, a Chechen who serves as Russian President Vladimir Putin's special adviser on the North Caucasus region, said on Wednesday.
Concerning the prospects for a political settlement, however, Maskhadov's loss may have real impact.
He was seen as a relative moderate in comparison with Basayev and had repeatedly called for negotiations to end the fighting.
Maskhadov was killed in a special
operation by Russian forces
His suggestions that compromise was possible - and the fact that he was Chechnya's elected president for a brief period of de facto independence and relative calm - lent him credibility and support among those Chechens tired of the conflict.
"For me, the death of Maskhadov is a great pain. He was aiming for peace and wanted to achieve it, but the Kremlin didn't want this," a resident of the Chechen capital Grozny, who gave his name only as Shudin, said.
Maskhadov was blamed by Moscow for deadly attacks too - but he usually denied the charges.
Basayev, by contrast, has taken part in and claimed credit for some of the deadliest attacks, including the Beslan school hostage-taking that left about 330 people dead last year, and the 2002 seizure of hundreds of hostages at a Moscow theatre.
"A new period has begun in the modern history of the Russian-Chechen military confrontation, which not only allows for no negotiations, but also for no end to the war "
With Maskhadov's "violent death ... a new period has begun in the modern history of the Russian-Chechen military confrontation, which not only allows for no negotiations, but also for no end to the war", Chechen separatist Movladi Udugov wrote on a separatist website.
Maskhadov's London-based envoy Akhmet Zakayev predicted that the new phase could bring more attacks.
"It's my personal fear that the radical part of the Chechen resistance, after what happened yesterday, will feel its hands untied and freed from any moral responsibility," he said.