Speaking at the opening of a meeting in Moscow of the Russia-NATO Council, Lavrov said Russia and NATO faced difficult work ahead on issues such as a key arms control treaty and U.S. missile-defense plans.
"These issues are related to key aspects of European and international security, to aspects of strategic stability," Lavrov said. "And of course, they have to be treated carefully, so that each other's stability and security is treated with care and that no steps are taken that would aim at strengthening the security of one at the expense of the other."
Moscow and NATO disagree sharply on U.S. plans to deploy parts of a missile-defense system in Poland and the Czech Republic.
Washington says the system would guard against potential missile attacks from Iran, while Moscow says Russia is the real target.
Another dispute is over a Soviet-era treaty limiting military deployments between the Atlantic Ocean and the Ural Mountains.
The Conventional Forces in Europe Treaty, first signed in 1990, was amended in 1999 to reflect the breakup of the Warsaw Pact and NATO expansion.
NATO members, however, have declined to ratify the amended treaty until Russia withdraws its troops from Moldova and Georgia. Russian President Vladimir Putin in April announced Russia was suspending its participation in the pact.
However, both Lavrov and NATO Secretary-General Jaap de Hoop Scheffer stressed the need to maintain dialogue on key disagreements between Russia and the alliance.
"We should continue discussions on subjects where we do not see eye-to-eye, be it Kosovo, be it missile defense, be it the Conventional Forces in Europe Treaty," de Hoop Scheffer said.
"That is what the [NATO-Russia Council] is for, it's not only to say how much we agree, but it is also for a serious, open, and frank discussion about where we do not agree," he said.
NATO wants Russian troops to leave Georgia and Moldova (TASS)
Today's meeting marked the fifth anniversary of the founding of the NATO-Russia Council, and the 10th year of partnership.
Commemorative events started with a special NATO-Russia seminar in St. Petersburg on June 25.
In St. Petersburg, de Hoop Scheffer addressed NATO's stance on some of those problems. He reiterated that "the door is open" to new members of the alliance, despite Russian concerns.
As for the U.S. plans to base parts of a missile-defense system on the territories of NATO members Poland and the Czech Republic, de Hoop Scheffer said during a debate broadcast by Russia's Ekho Moskvy radio that "You don't have to be Einstein to understand that 10 interceptor rockets don't pose any threat to Russia and the Russian people."
De Hoop Scheffer will have the opportunity later today to express his views to the Russian president himself. Observers have speculated that de Hoop Scheffer will seek to gauge Putin's position ahead of the Russian leader's face-to-face with U.S. President George W. Bush in Maine on July 1-2.
(with agency reports)
AN RFE/RL VIDEO PRESENTATION: The Czech Republic responds to the U.S. missile-defense proposal.