Maskhadov was killed last week in a special operation in the village of Tolstoy-Yurt, in northern Chechnya. The security service had announced in September that it would pay the reward for tips on the top rebel leader's whereabouts.
The security service's press office said Tuesday that the agency would be prepared to help the people who provided the information to move to another region of Russia or to a Muslim country. It was unclear how many people would split the reward.
"The Russian Federal Security Service confirms its preparedness to guarantee personal security and payment of an appropriate monetary award to citizens providing trustworthy information on the whereabouts of the terrorist leaders," the press office said.
The killing of Maskhadov, one of Russia's most-wanted men, was a victory for the security services, who have struggled to penetrate the tightly-knit clan society of Chechnya. Maskhadov and other rebel leaders appeared able to move about fairly freely in the region, where they boasted of a large network of collaborators.
The announcement of the reward came a day after authorities said they had blown up the house where Maskhadov was killed because they feared the building could have been booby trapped. But rights activists and government critics questioned the motives for the building's destruction, which added to the secrecy surrounding last week's raid.
Col.-Gen. Arkady Yedelev (search), chief of the federal headquarters for the campaign in Chechnya, said Monday that demolition experts who inspected the bunker where Maskhadov was said to have been hiding had discovered and detonated a box that contained documents and was riddled with explosives.
"The team of investigators decided to blow up the entire house to avoid such surprises in the future," Yedelev said in a statement.
Federal troops arrived Sunday in several trucks and armored vehicles, ordered residents of neighboring buildings to clear the area and then blew up the house in a powerful blast, witnesses said.
A neighbor, who identified herself only by her first name, Zura, said the explosion shattered windows and cracked walls in her house. "It scared me and my children to death," she said.
While federal authorities said Maskhadov was hiding in the bunker, Yakha Yusupova — who lived in the house with her family — denied the rebel leader had been there and said she suspected Russian forces may have brought him on Tuesday.
Anna Politkovskaya, a prominent Russian columnist and expert on Chechnya, said the house was apparently blown up to destroy any evidence that could cast doubt on official accounts of Maskhadov's killing.
"There is nothing left now to question the official version of events," Politkovskaya said in a telephone interview, scoffing at the official explanation.
"Can't they defuse booby traps without blowing up the entire house?" she said.
Alexander Petrov of Human Rights Watch's Moscow office said federal authorities in the past had blown up houses in Chechnya that belonged to militants who participated in attacks. The practice has drawn strong criticism from international rights groups, he said.
"If the authorities blew up the house to punish the house owners, it's a bad move," Petrov said.
Several prominent Russian rights activists on Monday joined Maskhadov's family in calling on Russian authorities to return his body for burial.
"Refusing to hand over the body to the relatives of the deceased is a shame," representatives of three rights groups wrote in a statement carried by the Interfax news agency.
They also criticized the security services for killing the rebel instead of capturing him.
"Considering the technical equipment special forces have, Maskhadov could have been captured alive and could have stood trial," they said.