* U.S.-Russia talks held under strains over Snowden affair
* Lavrov describes mood as positive overall
* Both say Syria government, rebels must negotiate a peace (Recasts after meeting with Lavrov comments)
By Paul Eckert and Susan Cornwell
WASHINGTON, Aug 9 (Reuters) - U.S. and Russian officials agreed on Friday on the need to convene a Syrian peace conference in Geneva as soon as possible and will meet again by the end of the month to prepare for the talks, Russian Foreign Minister Sergei Lavrov said.
Lavrov said the mood of talks in Washington between the top U.S. and Russian diplomatic and defense officials was very positive. The meeting opened after days of recriminations over Moscow's decision to grant asylum to former U.S. spy agency contractor Edward Snowden.
Both Lavrov and U.S. Secretary of State John Kerry acknowledged their sharp differences over Snowden and other issues going into the talks, which also included Defense Secretary Chuck Hagel and his Russian counterpart Sergei Shoigu.
"Edward Snowden did not overshadow our discussions," Lavrov told reporters, adding that he believed that case should not affect "mainstream" U.S.-Russia relations.
As the so-called "2+2" talks opened, Kerry said the two countries need to find ways to work around their sharp differences and make progress on missile defense, Afghanistan, nuclear disputes with Iran and North Korea and the two-year-old civil war in Syria.
"This meeting remains important above and beyond the collisions and the moments of disagreement," said Kerry.
While Washington and Moscow differ on key aspects of the Syria crisis, Kerry said, "Both of us and our countries agree that to avoid institutional collapse and descent into chaos, the ultimate answer is a negotiated political solution."
The talks at the State Department opened as the political mood between the two countries hit one of its lowest points since the end of the Cold War.
President Barack Obama's cancellation this week of a summit in Moscow over President Vladimir Putin's decision to give Snowden asylum put to rest any notion that a much-vaunted "reset" of ties with Moscow sought by the United States in recent years is alive.
Moscow and Washington disagree over a long list of issues, from Syria's civil war to human rights and Russia's ban on homosexual "propaganda." But there are some areas, critical to global security, where they have been able to work together.
Hagel and Shoigu held talks earlier on Friday, and both said they agreed to work to expand military-to-military cooperation. (Additional reporting by David Alexander; Editing by Philip Barbara and Vicki Allen)