* US-Russia talks in Geneva aim to seal deal on fighting Islamists

* "Still issues that need to be ironed out," U.S. official says

* Kerry hopes plan will hasten aid deliveries and political track

(Adds quote from senior U.S. official, start of meeting)

By Lesley Wroughton and Stephanie Nebehay

GENEVA, Aug 26 (Reuters) - U.S. Secretary of State John Kerry and his Russian counterpart Sergei Lavrov met in Geneva on Friday to try to hammer out final details of a cooperation agreement on fighting Islamist militants in Syria.

The hope is that a deal on fighting jihadists in Syria will help lead to a cessation of hostilities between the army and its militia allies on one side and non-jihadist rebels opposed to President Bashar al-Assad, as a step towards relaunching talks on a political transition to end the five-year Syrian conflict.

The meeting between Lavrov and Kerry at a luxury hotel on Lake Geneva began shortly after 10 am (0800 GMT). Asked what the main impediment was to a nationwide ceasefire, Lavrov quipped: "I don't want to spoil the atmosphere for the negotiations."

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 as the talks began.

"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 the fighting that is driving thousands of Syrians into exile in Europe and preventing humanitarian aid from reaching tens of thousands more, as well as preserving a political track.

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.

The advance westward in the next phase of their Turkey-backed operation could take weeks or months to complete, a rebel commander told Reuters.

Turkish military shelled the Kurdish militia, the People's Protection Units, or YPG, south of Jarablus and demanded that the YPG retreat to the east side of 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.

By reaching a deal with Russia, which supports Syrian Assad, Washington hopes that it will help launch talks on a political transition in Syria.

On Thursday, the UN said Russia had agreed to a 48-hour humanitarian ceasefire in the divided Syrian city of Aleppo to allow aid deliveries, although U.N. officials said they were waiting for security guarantees from parties on the ground before moving forward.

The United Nations has pushed for a weekly pause in the fighting in Aleppo to deliver food, water and medicine to civilians caught in the fighting.

Separately, Syrian rebels and government forces agreed in a deal on Thursday to evacuate all residents and insurgents from the besieged Damascus suburb of Daraya, ending one of the longest standoffs in the five-year conflict.

(Reporting by Lesley Wroughton; Editing by Peter Cooney and Dominic Evans) ((lesley.wroughton@thomsonreuters.com; +1-202-898-8393;))