The government had initially resisted the theory that the plane fell victim to terrorism, perhaps in retaliation for Russia's support of the government of Bashar al-Assad
But in a turnaround, the government is offering the reward, according to the official Sputnik news.
Also on Tuesday, a U.S. defense official said Russia had conducted a "significant number of strikes" in Raqqa in northern Syria in the past several hours. The terrorist group ISIS
, which has claimed responsibility for downing the plane, has made its Syrian headquarters in Raqqa.
The group's claim has yet to be verified. It has also claimed responsibility for the massive terrorist attack in France on Friday, in which at least 129 people were killed.
Metrojet Flight 9268 crashed
on October 31 after departing from the Egyptian resort of Sharm el-Sheikh, killing all 224 people
Putin: 'We remember everything'
The head of the FSB, Aleksandr Bortnikov, said the homemade bomb had the explosive power of one kilogram of TNT, according to the Kremlin.
The remarks came in a meeting Russian President Vladimir Putin
held with various security and foreign affairs officials -- a meeting that began with a minute of silence for the victims of the crash.
The bomb, Bortnikov told Putin, explained why fragments of the plane were scattered over a large area, the Kremlin website said.
"This is not the first time Russia experiences barbaric terrorist crime, usually without any obvious internal or external causes, the way it was with the explosion at the railway station in Volgograd at the end of 2013." Putin said. "We remember everything and everyone."
He said Russians would not dry their tears, but would nevertheless find and punish those responsible.
"We have to do it without any period of limitation; we need to know all their names," Putin said. "We will search wherever they may be hiding. We will find them anywhere on the planet and punish them."
He told the Foreign Ministry to appeal for international help.
'Security has got to be enhanced'
Western governments, particularly those in Britain and the United States, had said they had information pointing to a bomb having brought the plane down, and have said it may have been smuggled aboard the plane in Sharm el-Sheikh, from which the plane took off -- possibly with help from an airport employee.
They have criticized security procedures at the airport at Sharm el-Sheikh. The plane was bound for St. Petersburg, Russia.
Reuters, citing security officials, reported Tuesday that two Sharm el-Sheikh airport employees had been detained in connection with the Metrojet investigation. But Egyptian authorities denied the report.
Both a spokesman in Egypt's Interior Ministry and a spokesman in Egypt's Civil Aviation Ministry denied to CNN that any arrests have been made in connection to the crashed plane.
CNN spoke Tuesday with Carolyn McCall, chief executive of the UK budget airline EasyJet, who has called for aviation security and regulation to be improved.
"The reason the British government advised all airlines to stop flying to Sharm is that they believed there was a device in the hold of the Metrojet aircraft," McCall said. "They had inside intelligence giving them that information, so that's not surprising to anybody in the airline industry, given that the British government took very strong action immediately. Clearly, that is why security has got to be enhanced at Sharm el-Sheikh."
She said EasyJet had suspended flights to Sharm el-Sheikh through the end of this month, as have all other British airlines.
"We will not resume flying until we are told unequivocally by the government that it is safe to operate at Sharm el-Sheikh airport," she said.