Sen. Richard Lugar (R-Ind.) said Tuesday that President Obama's first trip to Russia has "gone well" and could lead to better relations between the two former Cold War adversaries.

Lugar, the top Republican on the Senate Foreign Relations Committee, praised the agreement announced Monday between Obama and Russian President Dmitry Medvedev to reduce their countries' nuclear arsenals by at least one quarter.

"I appreciated the reports that came yesterday and the way they have framed the issue," said Lugar, who worked with Obama when he was a senator on nuclear arms control.

"I'm hoping they will be able to finish the work in a timeframe so that a proper ratification of the treaty can occur both in Russia and in the United States," Lugar told The Hill.

The Republican said that the two countries have a sound relationship when it comes to curtailing the spread of nuclear weapons.

"Both countries see a win-win issue there," he said. "This is a foundation on which to have other conversations, such as missile defense."

He noted that the two countries have struck smaller deals on weapons, including agreements to destroy 34 tons of plutonium each and improve the fortification of nuclear agencies around the world to protect against arms proliferation.

"These were all areas where there can be a more cordial atmosphere to tackle other issues perhaps down the trail," he said.