MOSCOW (Reuters) - A militant group that claimed responsibility for last month's suicide bombings in Volgograd which killed at least 34 people told Russians on Saturday to rebel against President Vladimir Putin or face further attacks.

The warning, which came two weeks before the Winter Olympics in Russia's southern city of Sochi, does not mention the Games.

But the group - which identified itself as Vilayat Dagestan from the northern Caucasus region where Moscow has battled an insurgency for over a decade - last week warned Putin to expect a "present" at the event.

Putin has staked much personal and political prestige on the Games in Sochi, on the western edge of the Caucasus mountains. The event is expected to cost Russia more than $50 billion and is intended to show how far the country has come since the collapse of the communist Soviet Union in 1991.

In a statement posted on its website on Saturday, Vilayat Dagestan said the two Volgograd bombings, of a train station and a trolley bus, were a response to "atrocities carried out by the disbelievers on the ground of the Caucasus".

"Gone are the days when it was possible to destroy Muslims gratuitously," it said. "Today, one mujahid could destroy dozens or even hundreds of people in your cities. And do not think that these are isolated cases and that you will not feel the losses. The number of such bombings will only grow, and they will overtake many of you."

"The Kremlin gang leaders make cannon fodder of you and your children, while they themselves accumulate billions in this war," said the group, whose name means "Province of Dagestan".

"If you do not decapitate this hydra, you will not see a quiet life," it said.

Russian security officials declined to comment.

Dagestan is a mainly Muslim province at the heart of the insurgency to create an Islamist state in the North Caucasus and is racked by almost daily violence.

Russia has repeatedly said the Sochi Games will be safe, with Olympic Committee chief Alexander Zhukov saying last week that "all necessary security measures have been taken and safety will be ensured".

At least five European countries' Olympic committees received letters last week making a "terrorist threat", but Russia dismissed the warnings as a hoax.

(Reporting by Lidia Kelly; Editing by Pravin Char)