Russian President Vladimir Putin and United States Secretary of State Condoleezza Rice agreed Tuesday to improve bilateral ties though differences still remain after their talks.

The two agreed that "rhetoric in public exchanges should be toned down and we should focus on concrete issues," including non-proliferation, Russian Foreign Minister Sergei Lavrov, who also took part in the meeting, was cited by the RIA Novosti news agency as saying.

"We did talk about the need to keep the temperature down," Rice told reporters after the meeting at the presidential residence in Novo-Ogaryovo outside Moscow.

Russia and the United States "sometimes have opposing attitudes to certain problems, but their cooperation is still efficient," the Interfax news agency quoted First Vice-Premier Sergei Ivanov as saying on Tuesday.

"An opinion that Russia-U.S. relations are lapsing into another Cold War is wrong," Ivanov said, a day after his meeting with Rice in Moscow, echoing Rice's rejection to the suggestion of a "new Cold War" when she was heading for Moscow early Monday.

However, arrays of disputes which has steered bilateral ties between the Cold War rivals to a downturn, such as U.S. plans to deploy an anti-missile system in central Europe, seemed to remain unresolved during the top U.S. diplomat's two-day trip.

"(President Putin) confirmed Russia's position on missile defense," Lavrov said after the meeting.

Moscow maintains that the missile-defense plan, including 10 interceptor missiles in Poland and a radar station in the Czech Republic, is endangering its own security and the regional situation as well. The United States denies this, saying that it is designed to fend off threats from nations such as Iran.

Rice, however, said the United States is determined to do so.

"I don't think anyone expects the United States to permit somehow a veto on American security interests," she told reporters after meeting Putin.