U.S. President Barack Obama meets with Russian Prime Minister Vladimir Putin in Moscow on Tuesday. (Jim Young/Reuters)

The United States and Russia must overcome the mistrust and rivalry that dates back to the Cold War and forge ahead with a renewed relationship, U.S. President Barack Obama told students in Moscow on Tuesday.

Speaking at the New Economic School, Obama said the two countries are not "destined to be antagonists" in the 21st century.

"The pursuit of power is no longer a zero-sum game," the president said.

Obama has been using his trip to Moscow in an attempt to renew relations between the U.S. and Russia.

But any "fresh start" in U.S.-Russia relations can't just happen at the government level and must have the support of the people, Obama said.

U.S. President Barack Obama delivers remarks at the New Economic School graduation in Moscow on Tuesday. (Jim Young/Reuters)

The status of the relations between the two countries will largely be determined by citizens, he said.

"You get to decide what comes next. You get to choose where change will take us," Obama said. "The future does not belong to those who gather armies on a field of battle or bury missiles in the ground. The future belongs to young people with the education and imagination to create."

'Progress must be shared'

Obama — who is not well-known in Russia and whose trip has gone largely under the radar in the country's tightly controlled media — focused his speech on defining the United States' place in the world. He said the U.S. and Russia share interests and that "progress must be shared."

Obama told the graduating students that Russia and the United States share similar interests in halting the spread of nuclear weapons, confronting violent extremists, ensuring economic prosperity, advancing the rights of people and fostering co-operation without jeopardizing sovereignty.

During the first day of the two-day summit — the first between the two countries in seven years — Obama and Russian President Dmitry Medvedev signed an agreement to cut their nuclear weapons stockpiles by as much as one-third within seven years.

The U.S. and Russia must also stand united in resisting North Korea's attempt to become a nuclear power and Iran's efforts to obtain nuclear weapons, he said.

Obama added an end to Iran's nuclear efforts would eliminate the need for a missile defence system in Europe. Russia has demanded the U.S. plan be scrapped before implementation of any replacement for Strategic Arms Reduction Treaty (START I), which expires on Dec. 5.

Meeting with Putin

Getting rid of weapons of mass destruction is the "nuclear challenge of the 21st century," Obama said.

Earlier on Tuesday, Obama met with Russian Prime Minister Vladimir Putin for a private discussion over breakfast.

The two talked about Georgia and Ukraine "and generally about the post-Soviet area," said Yuri Ushakov, an aide to Putin.

Though protocol does not demand the president visit the prime minister, many analysts see Putin as still holding the real reins of power in Russia.

White House officials said Obama "formed the basis of a good relation" with Putin during the two-hour meeting.

Obama also met with former Russian president Mikhail Gorbachev and members of opposition parties. He and Medvedev then attended a meeting with business and civic leaders, where the U.S. president urged more transparency to ensure economic growth and investment.

Obama is travelling with his wife, Michelle, and his daughters, Sasha and Malia, during the week-long trip.

Following Obama's meetings in Russia, he will travel to Italy for G8 meetings on Wednesday and then head to Ghana to deliver a speech on Thursday.

With files from The Associated Press