Russia's granting of temporary amnesty to former U.S. spy agency contractor Edward Snowden should not be allowed to affect Moscow-Washington ties, a Russian lawmaker said Thursday.

"Snowden's activity isn't worth cooling relations between our countries," Mikhail Margelov, head of the International Committee of the Federation Council (upper house of the parliament), said.

Margelov said, even during the Cold War, neither Soviet dissidents flying to the West nor U.S. dissidents supported by Moscow hampered summits.

Great powers understood their responsibility over nuclear arms control, regional conflicts, militarization of space and other global issues, the politician told Interfax news agency.

"Now there are no fewer global problems requiring face-to-face meetings of the U.S. and Russian leaders than it used to be during the Cold War," Margelov said.

He added the upcoming so-called "2+2" meeting of the two countries' defense and foreign ministers due in Washington on Friday could "hopefully" minimize the damage incurred by the U.S. pulling out of next month's scheduled summit between U.S. president Barack Obama and Russian counterpart Vladimir Putin.

According to Margelov, the value of these summits lie not only in the decisions made but in the very fact that they take place.

"They send signals to the international community that dialogue between two leading powers remains ongoing," the senator said.

Also Thursday, head of the International Committee of the parliament's lower house, or State Duma, Alexei Pushkov said Obama's aborted visit meant the "burial" of the reset policy.

"The relations need a new program. Putin and Obama could be discussing it in Moscow. Instead, the U.S. administration decided to take a negative pause in relations, but this does not help resolve a single problem," Pushkov said on his Twitter account.

The Kremlin said it was disappointed by Obama's withdrawal from the scheduled Moscow summit with Putin on the eve of the Group of 20 (G20) summit slated for Sept. 5-6 in St. Petersburg.