"We hope the constructive proposals that U.S. National Security Advisor James Jones made in Moscow last week would help bring our positions closer and forge a balanced document meeting the two countries' interests and strengthening international security," Andrei Nesterenko told the Interfax news agency.
"The atmosphere at the negotiations was business-like and constructive," he said, adding that "there is progress."
The spokesman did not reveal any details of the ongoing negotiations, as both sides agreed to keep the discussions confidential from the very start.
Meanwhile Nesterenko also pointed out several remaining disagreements between Russia and the United States.
He said Russia insisted that the new treaty should "primarily stipulate a lower ceiling of strategic delivery vehicle," and the link between strategic offensive and defensive weapons should be reflected appropriately in the new treaty.
Russia and the United States will start their eighth round of negotiations on nuclear arsenal cuts Nov. 9 in Geneva.
The START-1, signed in 1991, obliges the U.S. and Russia to reduce their nuclear warheads to 6,000 and delivery vehicles to 1,600.
Russian President Dmitry Medvedev and his U.S. counterpart Barack Obama agreed at a July summit in Moscow on the outline of the new arms cuts treaty, including slashing their countries' nuclear arsenals to 1,500-1,675 operational warheads and delivery vehicles to 500-1,000.