Lisbon, Portugal (CNN) -- President Obama and Russian President Dmitry Medvedev met privately on the sidelines of a NATO summit Saturday, a national security advisor said.
The private conversation came as the START treaty, a proposed nuclear pact between the United States and Russia, emerged as a major topic at the summit in Lisbon, Portugal.
"They were able to go aside into a room by themselves and talk for 15 to 20 minutes," deputy national security advisor Ben Rhodes said. "The two leaders have developed a very strong rapport."
Obama wanted to get some time alone with Medvedev before the press conference and after the meeting, Rhodes said.
Officials aboard Air Force One told reporters that the treaty came up during the conversation, which Obama later described as "very cordial."
The treaty would restart mutual inspections, while limiting both nations to 1,550 warheads and 700 launchers each.
Obama has called ratification of the treaty a priority during Congress' lame-duck session, saying it's critical to national security and a cornerstone of U.S.-Russia relations.
But 10 GOP senators, led by Sen. Jon Kyl of Arizona, have urged a delay until the next Congress over concerns about the current congressional workload and over-modernization of the U.S. nuclear arsenal.
Obama emphasized the need for the treaty to be adopted. He told reporters at the summit that Kyl wants a "safe and secure America just like I do" and never said to him that Kyl's opposed to the treaty.
But Obama said he has received "overwhelming support from our allies here that the new START treaty is a critical component" to U.S. and international security.
NATO Secretary-General Anders Fogh Rasmussen said a delayed ratification "will be damaging to the overall security environment in Europe."
"We strongly urge both parties to ratify the START treaty as early as possible," he said.
Russia and NATO agreed Saturday to work closely on the crucial issue of missile defense.
Medvedev agreed that the two sides will exchange information and work with each other to defend themselves.
Obama and Rasmussen also said both entities will step up cooperation across the board, including Russia's agreement to allow non-lethal NATO supplies to and from its territory for the war effort in Afghanistan.
"We see Russia as a partner, not an adversary," Obama said.