Konstantin Kosachyov, who leads the international affairs committee of the lower house of parliament, was commenting on Western media reports that U.S. President Barack Obama was set to propose to Russia a significant reduction in nuclear warhead numbers.
Citing sources in Washington, The Times said that the U.S. administration would like the number of nuclear warheads on both sides cut to 1,000, or an 80% reduction.
Kosachyov also said he welcomed "the general mood for a reduction in nuclear armaments," but said the reductions on both sides should be balanced.
Grigory Karasin, a deputy Russian foreign minister, said on Wednesday that Russia viewed as an important and positive signal reports concerning the Obama administration's desire to reduce nuclear arsenals.
The Times also quoted Russian Deputy Prime Minister Sergei Ivanov as saying on Wednesday that Russia welcomed the Obama administration's proposals to expedite the signing of a new treaty on strategic arms reduction.
The Strategic Arms Reduction (START-1) Treaty signed between the Soviet Union and the United States in 1991 expires on December 5, 2009.
It places a limit of 6,000 strategic or long-range nuclear warheads on each side, and limits the number of delivery vehicles, such as bombers, land-based and submarine-based missiles, to 1,600 each.