During the meeting, Putin told the UN chief that Russia considers the United Nations "the key element of today's entire international system."
"Russia and the UN enjoy very close relations and Russia is not only a founding member of the UN, but one of its most active," Putin said.
Ban ki-Moon, who is in Moscow on a two-day official visit, had met earlier in the day with Russian president-elect Dmitry Medvedev to discuss Moscow's role in the UN.
Medvedev will become president on May 7 when Vladimir Putin steps down. Putin is expected to be approved by parliament as Russia's premier a day later.
During the meeting with Ban, Medvedev raised the issue of Kosovo, which unilaterally declared its independence from Serbia on February 17, saying that its recognition by a number of countries, including the U.S. and the majority of EU nations, had violated UN resolutions.
"Any attempts to solve international problems through a violation of UN resolutions... are counterproductive and do not contribute toward achieving peace and stability in the world," the president-elect said.
"You are right that no nation, however powerful and resourceful it is, can resolve all problems," Ban answered.
Medvedev also said that Russia, as a permanent member of the UN Security Council, respected and valued the role of the UN in the modern world.
