In a speech on the state of U.S.-Russia relations, Rice conceded there was a "certain distance" between Washington and Moscow, but she rejected suggestions there had been a return to the frosty ties of the Cold War era.
Russia is a key energy supplier in Europe but it has reduced or even cut supplies over a range of disputes with neighboring countries. For example, this month, it threatened to reduce supplies in a dispute with Kiev over payments.
"We respect Russia's interests, but no interest is served if Russia uses its great wealth, its oil and gas wealth, as a political weapon or that treats its independent neighbors as part of some old sphere of influence," said Rice, an expert on the Soviet Union.
The former Soviet Union broke up in the 1990s and Rice said Russia should not view that as a threat to its own stability.
"Nor do we believe that Europe's unity and liberty since 1991 is unjust. The freedom of people to choose their own governments and the freedom of governments to make their own way is a source of security and not a threat to it," said Rice, who was in Moscow little over a week ago.
"Russia has regained some of its strength and its cohesion. But at times, perhaps reflecting the views of the 1990s, we fear that this is sometimes seen in zero sum terms of another era," she added.
The United States and other Western governments are concerned about democracy and human rights under President Vladimir Putin, who has consolidated the Kremlin's power.
STRONGER JUDICIARY, MEDIA
Rice urged Russia to strengthen the independence of its institutions, such as the judiciary and the media, and said such a move would improve relations.
"We want Russia to be strong, strong in 21st century terms, not just with a strong center but with strong, independent institutions, an independent judiciary and legislature, and an independent civil society and media and vibrant nongovernmental sector" she said.
Rice, who visited Russia this month along with Defense Secretary Robert Gates, said she hoped Moscow could work more cooperatively on trying to resolve the Kosovo problem.
"We hope that Russia will also realize that we can work together for a Kosovo solution that contributes to peace in Europe," she added.
She called for a greater understanding between the United States and Russia and sought to play down talks of a new Cold War.
"It's not to say that we don't have differences, we do. Yet Russia is not the Soviet Union," she said.
Russia-U.S. relations have been strained in recent months, particularly over Moscow's objection to U.S. plans to build a missile defense system in Europe.
But Rice pointed to closer cooperation with Moscow on tackling North Korea's nuclear program and on the Middle East.
While there were differences on tactics on how to get Tehran to give up their nuclear weapons program, she said Moscow and Washington both shared a common goal of preventing Iran from getting an atomic bomb.
The United States is pushing hard for a third U.N. Security Council sanctions resolution against Iran while Russia wants to give Tehran more time and is balking at more punitive measures.