But the two diplomats admitted that differences in their positions remained.
Mrs Clinton said the relationship between the two countries needed "more trust, predictability and progress".
After the talks, Mr Lavrov later told the 65-nation UN Conference on Disarmament in Geneva: "The right moment has come, for the first time since the end of the Cold War, for making real progress in resuming the global disarmament process on a broad agenda."
The BBC's Imogen Foulkes in Geneva says agreement on the need for a new deal to cut warheads and delivery systems by the end of this year is the easiest disarmament move the two sides can make at this point.
Other more divisive issues remain, says our correspondent, such as Washington's plan for a missile defence shield in Eastern Europe - Moscow strongly objects to this.
Clinton 'thrilled' with EU meetings
But, Sergei Lavrov said, talks are continuing on this too, and compromise might be possible.
Our correspondent says it is at least a sign the UN disarmament process, in stalemate for so long, is now moving again, amid warming relations between Moscow and Washington.
On Thursday, Nato agreed to resume high-level contacts with Russia, especially regarding co-operation over the Nato mission in Afghanistan.
Relations between the US and Russia have deteriorated in recent years over Russia's role in the war in Georgia, American support for the entry of Georgia and Ukraine to Nato, and the planned US missile shield based in central Europe.
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