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The closed-door talks were opened at the Russian mission to the United Nations Office in Geneva, and they would later be transferred to the U.S. mission, diplomatic sources said, adding that discussions may last two weeks.
Five rounds of full-fledged talks have been held between the two sides since Russian President Dmitry Medvedev and his U.S. counterpart Barack Obama agreed in London in early April to start talks for a new arms reduction treaty.
During their last round of talks in Geneva, which were concluded on Sept. 2, negotiators discussed the parameters of a new treaty, formulating wording that the presidents could both agree to, according to the Russian Foreign Ministry.
START I, due to expire on Dec. 5, places a limit of 6,000 strategic or long-range nuclear warheads on both countries and allows the inspection of weapons.
Medvedev and Obama signed a framework document on additional reductions and limitations of strategic offensive arms during their Moscow summit in early July.
The document says each country plans to cut nuclear warheads to1,500 to 1,675 "within seven years to come."
The new round of talks between the two sides opened shortly after President Obama announced the abandonment of a Bush-era missile defense shield program in Eastern Europe.
Analysts said the U.S. move may help clear away one of the major obstacles for resetting relations between the two countries. It could also help promote progress of nuclear disarmament talks between the two sides.