Dmitry Medvedev and new U.S. leader Barack Obama will meet for the first time on the sidelines of the G20 summit of world leaders to address the financial crisis.
Media reports said earlier Washington had sought Russian help in resolving the nuclear dispute with Iran, and could in turn drop its plans to deploy a missile shield in Europe, strongly opposed by Moscow.
Both Moscow and Washington have officially denied the possibility of such a deal.
Speaking to a delegation of former U.S. senators, Medvedev also said Russia and the United States had every opportunity of opening up a new chapter in bilateral relations.
"The signals I have been receiving from the United States, from President Barack Obama, are quite positive," Medvedev said.
"We have a broad agenda, and too much [in global politics] depends on how Russia-U.S. relations develop," Medvedev said, mentioning arms control, efforts against terrorism and economic problems.
Gary Hart, a member of a bipartisan commission on U.S.-Russia relations which is to make a report on its visit to Obama next week, said at the start of the talks: "What brought us together is the feeling that the relationship between our two countries was not in the interests of the United States."
"We hope to build a base in our country that will give support to the new administration in its efforts to improve that relationship," Hart said.
Relations between the former Cold War archrivals have been strained in recent years over a host of differences, including the planned U.S. missile base in Poland and radar in the Czech Republic and Russia's armed conflict with U.S. ally Georgia in August.
The two countries' top diplomats made a symbolic "reboot" to improve ties when they met in Geneva earlier this month.
Foreign Minister Sergei Lavrov and Secretary of State Hillary Clinton pledged to try to come to terms on a new strategic arms reduction treaty to replace START-1 by the end of 2009, and vowed further cooperation in anti-terrorism efforts in Afghanistan, tackling Middle East crises, and resolving nuclear disputes with Iran and North Korea.