The United States is ready to help Russia's security operation for the Winter Olympics, the Pentagon said Saturday, after twin suicide bombings sparked concern next month's extravaganza could be targeted.

US Secretary of Defense Chuck Hagel offered American support during a phone conversation with his Russian counterpart Sergei Shoigu, the Pentagon said.

Hagel's phone call came after separate bombings in the southern Russian city of Volgograd on Sunday and Monday which left 34 people dead.

"Secretary Hagel offered his condolences for the recent terrorist attacks in Volgograd," Pentagon Press Secretary Rear Admiral John Kirby said.

"The leaders discussed the need to remain vigilant against these threats and considered additional opportunities to deepen our nations’ counterterrorism cooperation.

"Secretary Hagel also assured Minister Shoigu that the United States stands ready to provide security assistance to Russia for the Winter Olympics in Sochi, if requested."

The Olympics will be held in Sochi, some 425 miles (700 kilometres) southwest of Volgograd, from February 7 to 23.

Hagel and Shoigu also discussed the international operation to dismantle Syria's chemical weapons stockpile, the Pentagon said.