* No let-up in violence for Eid holiday
* Air force strikes across the country
* Fighting hampers chemical weapons team
By Dominic Evans
BEIRUT, Oct 15 (Reuters) - Syrian air force jets and helicopters bombed rebel-held districts across the country on Tuesday, the first day of the Muslim festival of Eid al Adha, and rebel fighters fired rockets into the heart of Damascus.
President Bashar al-Assad, whose forces are battling a civil war which grew out of protests against his rule two years ago, was shown on state television attending morning prayers with ministers at a Damascus mosque at the start of the Eid holiday.
But there was no let-up in the violence which has torn Syria apart and divided the Middle East between Sunni Muslim supporters of the rebels and Shi'ite backers of Assad, despite a joint plea from regional Arab and Muslim organisations for both sides to mark the occasion with a ceasefire.
Activists said warplanes bombed targets in rebel strongholds to the east and south of the capital. Video footage uploaded on the Internet showed explosions and thick columns of smoke rising above the town of Daraya, on the southwestern edge of Damascus.
Rebels fired rockets and mortars into the Old City and the Mazraa district in the city centre, activists said.
The Syrian Observatory for Human Rights, which monitors the violence in Syria through a network of activists and medical and military sources, also said air force helicopters carried out 11 bombing raids on the rebel town of Latamna in Hama province.
It said the helicopters dropped large improvised explosives, or barrel bombs, on the town. Three children were killed in one of the early waves of bombing, it said.
The Observatory says at least 115,000 rebels, soldiers and civilians have been killed in the 2-1/2 year civil war which has also driven 2.1 million Syrians to seek refuge abroad and displaced millions more inside their country.
A further 170 people were killed on Monday, it said.
REBEL CLASHES ON BORDER
The fighting also pits rival rebel factions against each other. On Tuesday activists said militants from al Qaeda-linked Islamic State in Iraq and the Levant clashed with local Northern Storm fighters at the Bab Salam border post with Turkey.
Video footage showed grey smoke rising from what the activists said were Northern Storm positions which had been shelled by the Islamic State fighters. The clashes were close to a refugee camp on the Syrian side of the border, they said.
The divisions among Assad's opponents and the growing power of the Islamist fighters have made it increasingly difficult for international aid workers to operate in the lawless rebel-held northern provinces.
Six Red Cross workers and a colleague from the Syrian Arab Red Crescent were abducted on Sunday after delivering medical supplies in the northern province of Idlib. Four were released the next day but an ICRC spokesman said on Tuesday there was no news on the other three.
The violence has continued despite a U.N.-endorsed mission to oversee the elimination of Assad's chemical weapons, which was set up as a result of a rare agreement between the United States and Russia after an August sarin gas attack in Damascus.
Experts from the Organisation for the Prohibition of Chemical Weapons have visited eight of a total of around 20 sites where they are due to oversee the destruction of Syria's chemical arsenal and production facilities.
Some of the destruction work has already started and the OPCW - which last week was awarded this year's Nobel Peace Prize - has reported that Syrian authorities have so far cooperated with the process.
However the most complex stage of their work, the destruction of chemical agents and precursors, has yet to start and the teams will likely have to visit at least one site - near the northern town of Safira - where fighting is continuing.
The Observatory said on Sunday that Assad's forces bombarded rebel-held Safira, which is located close to storage and production sites which are believed to be linked to Syria's chemical weapons programme.
Unless a local ceasefire can be agreed or government troops push the rebels back the chemical teams would face the prospect of trying to work in the midst of a conflict, close to rebel fighters whose ranks may include anti-Western jihadists.