U.S. Secretary of State John Kerry has said Washington still has "shared interests" with Russia, despite deteriorating relations, most recently over the case of fugitive intelligence leaker Edward Snowden.
Opening talks with the Russian foreign and defense ministers in Washington, Kerry said bilateral ties are facing some "challenging moments."
"It's no secret that we have experienced some challenging moments and obviously not just over the Snowden case. We will discuss these differences today for certain," Kerry said. "But this meeting remains important above and beyond the collisions and the moments of disagreement. It is important for us to find ways to make progress on missile defense, on other strategic issues including Afghanistan, Iran, on North Korea and Syria."
The meeting in Washington follows the announcement from the White House on August 7 that President Barack Obama was canceling a one-on-one meeting with Russian counterpart Vladimir Putin
scheduled for Moscow next month.
"Our agenda is rather broad and it includes, of course, issues where we have disagreements," Lavrov said. "We will continue to talk about them, calmly, as we should. I recall my first meeting with John in his current position when he said our countries share a special responsibility and a lot depends on us. So, we need to work together, as adults. This is what we're trying to do and we hope it will be mutual."
The meeting also included U.S. Defense Secretary Chuck Hagel and Russian Defense Minister Sergei Shoigu.
It is expected to focus on the situations in Afghanistan, Iran, and North Korea, and U.S.-European plans for a missile-defense shield that Russia strongly opposes.
Ties between the United States and Russia are strained over several issues, one being Russia's decision to grant Snowden, a former U.S. intelligence contractor, temporary asylum.
Snowden leaked classified information about U.S. global Internet- and telephone-surveillance programs and faces espionage charges in the United States.
Washington has also been frustrated by Moscow's continued support of Syrian President Bashar al-Assad amid the country's devastating civil war. The United States supports rebel factions in the country and wants to see Assad leave power.
Moscow, for its part, has been concerned for several years about the joint U.S.-European plan to build a missile-defense shield in Europe. Washington says the system is intended to protect NATO countries from a possible attack from Iran, but Moscow argues it could affect Russia's nuclear deterrent.
The United States has also expressed concern about what it says is a crackdown on civil society in Russia since Putin returned to the Kremlin last year. There have been increased protests in the United States over a Russian law adopted this summer that criminalizes the "propaganda" of homosexuality to minors.
That law and another requiring nongovernmental organizations that accept foreign funding and engage in "political activity" to register as "foreign agents" have led to calls for the United States to boycott the 2014 Winter Olympics in Sochi. The Obama administration has said it is not considering a boycott.
On August 8, Russian Sports Minister Vitaly Mutko defended the gay-propaganda law.
"I want to calm everyone down first of all, as in addition to this law on the territory of Russia, we have the Constitution of the Russian Federation that guarantees all citizens the right to a private life, guarantees that there will be no interference in this private life," Mutko said.
"This law is not intended to deprive citizens of any country, religion, or orientations of their interests and rights. This law is intended to ban the propaganda among youth, more than anything else."
Mutko added that the law should not affect the Sochi Games.
"I can assure you that the Olympic Games will take place at the highest level. All rights of all citizens will be protected, but the laws of any country whose territory you enter, must of course be observed," he said. "But I'll say it again -- this doesn't affect the athletes at all. Come and compete."
With reporting by Reuters, AFP, AP, and ITAR-TASS