By BRIAN ROSS, CHRIS GOOD and LEE FERRAN

Hours after a second bomb exploded in Russia, killing more than a dozen, the White House crafted a message of condolences to the Russian people that also included a veiled jab, echoed by other U.S. officials, about Russia's apparent failure to fully cooperate with American security teams ahead of the Winter Olympic Games in Sochi.

"The United States stands in solidarity with the Russian people against terrorism," said a written statement from White House National Security Council spokesperson Caitlin Hayden. "The U.S. government has offered our full support to the Russian government in security preparations for the Sochi Olympic Games, and we would welcome the opportunity for closer cooperation for the safety of the athletes, spectators, and other participants."

The carefully-worded missive comes just hours after two top terror experts wrote on ABCNews.com that U.S. officials have complained counter-terror cooperation with the Russians "could be better."

"There is little cause for optimism, however, as anti-Americanism is promoted from above in Russia; and as Russian counter-terrorism operations with the United States and its allies have fallen victim to the counter-productive climate that has prevailed in the wake of the Boston Marathon bombing," wrote Director of Homeland Security Policy Institute Frank Cilluffo and Deputy Chief of the LAPD's Counter-Terrorism Bureau Michael Downing.

At a press briefing today State Department spokesperson Marie Harf told reporters that State Department Diplomatic Security has been cooperating with Russia on Sochi's security preparations, but Harf declined to say if any additional measures are being taken in the wake of the recent bombings.

A military official said the military-to-military relationship between Russian and U.S. forces is "as good as it has ever been," but the same official did not go as far as to characterize the relationship as "good."

The Russian Embassy to the U.S. in Washington, D.C. denied Russian security services were not playing nice with their international partners.

"Russia is fully cooperating with all interested law enforcement agencies including those from the U.S.," the embassy said in an emailed statement. "We are sure that [the] Sochi Olympic Games will be held in a secure and peaceful atmosphere."

Though no group has taken responsibility for the recent bombings, Chechen Islamist leader Doku Umarov earlier this year called for new attacks against civilian targets in Russia, including the Sochi Games. Umarov urged his followers to "do their utmost to derail" the Sochi Olympics, which he described as "satanic dances on the bones of our ancestors."

The top Olympics official, International Olympics Committee President Thomas Bach, has not been deterred by the attacks, saying today said he was confident of Russia's ability to protect the Games.

"This is a despicable attack on innocent people and the entire Olympic Movement joins me in utterly condemning this cowardly act," Bach said. "I have personally written to the President of the Russian Federation, Vladimir Putin, to express our condolences to the Russian people and our confidence in the Russian authorities to deliver safe and secure Games in Sochi."

Putin, at the helm of a powerful and vast domestic security force, has maintained the Games will be safe and secure, but Cilluffo and Downing warned that Americans should go into the famed international competition "with eyes wide open."