By Lesley Wroughton and Stephanie Nebehay

GENEVA (Reuters) - U.S. Secretary of State John Kerry and Russia's Sergei Lavrov sought on Friday to finalize an agreement on fighting Islamist militants in Syria as the first evacuees left a besieged Damascus surbub under a plan which has aroused the U.N.'s concern.

A deal on fighting jihadists in Syria could help lead to an end to fighting between the army and its militia allies on one side and non-jihadist rebels opposed to President Bashar al-Assad. This could pave the way for talks on a political transition to end the five-year Syrian conflict.

As Kerry and the Russian foreign minister met at a hotel on Lake Geneva, residents and insurgents began to leave the besieged Damascus suburb of Daraya where civilians have been trapped since 2012, Reuters witnesses said.

Rebels and Syria's army agreed the plan on Thursday to evacuate all the 4,000 residents and some 700 insurgents from Daraya in the coming days, ending one of the longest stand-offs in the civil war.

But the United Nations was not consulted on the plan and U.N. Special Envoy Staffan de Mistura and U.N. humanitarian coordinator Stephen O'Brien, voiced deep concern about it on Friday.

Civilians should be evacuated only if their safety could be guaranteed and it was on a voluntary basis, they said.

"It is imperative that people of Daraya are protected in any evacuation that takes place, and that this takes place voluntarily," de Mistura, who leads U.N. political and humanitarian efforts in Syria, said in a statement after holding talks with Kerry and Lavrov.


Senior White House officials from the National Security Council (NSC) joined the talks between Kerry and Lavrov, which broke after four hours, but were set to resume later.

While Kerry said this week that technical teams from both sides were close to the end of their discussions, U.S. officials indicated it was too early to say whether an agreement was likely.

"There are still issues that need to be ironed out," a senior State Department official said.

"We're hopeful that today could see resolution on at least some of them, and that we can move this plan forward," the official said, "But we're mindful of the challenges."

When Kerry launched the Syrian cooperation talks in July during a visit to Moscow, the proposal involved Washington and Moscow sharing military intelligence to coordinate air strikes against Islamic State and grounding the Syrian air force to stop it from attacking moderate rebel groups.

Kerry believes the plan is the best chance to limit fighting that is driving thousands of Syrians into exile in Europe and preventing humanitarian aid from reaching tens of thousands more.

The talks take place just days after Syrian rebels backed by Turkish special forces, tanks and warplanes entered Jarablus, one of Islamic State's last strongholds on the Turkish-Syrian border.

Turkish military shelled the Kurdish militia, the People's Protection Units, or YPG, south of Jarablus and demanded the YPG retreat beyond the Euphrates River within a week.

The YPG had moved west of the river earlier this month as part of a U.S.-backed operation, now completed, to capture the city of Manbij from Islamic State.

Turkey's stance puts it at odds with Washington, which sees the YPG as a rare reliable ally on the ground in Syria.

(Additional reporting by Lisa Barrington in Beirut and Firas Makdesi and Kinda Makieh in Damascus; Editing by Richard Balmforth)