Aslan Maskhadov, former Chechen president and the man Moscow blames for the school massacre last year in Beslan is said to have been killed in the Chechen town of Tolstoy-Yurt.
So far the death has not been confirmed. Vladimir Putin is asking for further identification.
Chechnya's Moscow-appointed Deputy Prime Minister Ramzan Kadyrov told Interfax news agency the intention had been to take Mr Maskhadov alive but that he had been was killed by careless weapons-handling by his bodyguards.
Russia's FSB security chief briefed President Putin on the troops' operation in a Chechen village, but did not say how Mr Maskhadov was killed.
He told the president the FSB security services "today carried out an operation in the settlement of Tolstoy-Yurt, as a result of which "the international terrorist and leader of armed groups Maskhadov was killed, and his closest comrades-in-arms detained".
"Carry out additional identification tests, report back," Mr Putin ordered.
"If this information is confirmed, grant state awards to all those involved in the operation," the Russian leader said.
Maskhadov recently called for talks with Putin saying, "We think that 30 minutes of honest eye-to-eye talk would be enough to end this war, so as to explain to the Russian president what Chechens want. I believe he does not know." Russian officials have worried that an independence movement by Chechnya would trigger calls for seccession from other regions.
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