The pro-Russian Chechen administration and Russian military say there has been no major fighting between Chechen rebels and Russian forces since last week.
The Kremlin has issued no public response, but pro-Russian Chechen President Alu Alkhanov said on 5 February that if Maskhadov and Basaev really want to stop terror they should turn themselves in to police and surrender.
In an interview published by the Russian newspaper "Kommersant-Daily" today, Maskhadov said he is hoping for a response from the Russian government. The separatist leader has named a spokesman, Umar Khambiev, to head the delegation for talks with the Kremlin.
Khambiev told RFE/RL he believes it's in the Kremlin's best interest to start negotiations.
"We have showed and we continue to show that we are ready for negotiations. We are different from the people they portray us to be. We are ready for negotiations even today and solving all contentious questions. Otherwise this war will not end in the way Russia wants and it is dangerous for Russia itself," Khambiev said.
Khambiev said if the bid to start talks fails, Chechen militants are ready to continue fighting. He said his group is not fixated on establishing an "independent" Chechnya, but that the main aim of the resistance is to get guarantees for the existence of the Chechen nation.
"It is up to negotiators to find these guarantees. If the [negotiators] don't want to call it 'independence,' we fill find a different formula for that. All these questions might be resolved through negotiations. Our president says and not without reason that 30 minutes would be enough to talk with the president of the Russian Federation and end this war," Khambiev said.
Khambiev said persistent rumors about Basaev's death are not true and are part of what he called a "Russian disinformation campaign."
"In his interview [with 'Kommersant-Daily'], President Aslan Maskhadov said that it is the sixth time when Basaev was reportedly killed. It means Maskhadov denied the rumors and chose not to answer the question," Khambiev said.
Basaev has claimed responsibility for many terrorist attacks carried out in Russia in recent years, including last September's Beslan hostage siege in which more than 320 people were killed. Maskhadov condemned the Beslan siege, and has said Basaev should face trial for his role in the hostage taking.
Khambiev downplayed any disagreement between Maskhadov and Basaev. "There are no special disagreements except pointed out by the president [Maskhadov] himself [in his interview]. He said he could not accept the means used by Basaev, and first of all he is concerned about actions against the peaceful Russian civilians," Khambiev said.
Khambiev said for this reason Maskhadov is the best partner for the Kremlin. He said the cease-fire indicates Maskhadov is in complete control of the Chechen resistance.
Kirill Koktysh of the Moscow Institute of International Relations, however, said that in his opinion it is impossible to imagine that Maskhadov controls all of the militant groups in Chechnya. "He might control some militants, but the problem is that he is one of many [commanders]," Koktysh said. "On the whole, Chechnya is now in [an impossible situation] where everyone is fighting everyone else. Very big numbers of groups, clans, and [families] are fighting one another."
Koktysh claimed the amount of military activity in Chechnya depends more on money coming in from abroad to support the militants than on what Maskhadov says.
(RFE/RL's North Caucasus Service contributed to this report)