BEIRUT (AP) -- Syrian warplanes bombed rebel areas near Damascus on Thursday as President Bashar Assad's troops battled opposition fighters for control of the road linking the capital to the country's largest airport.

Assad's forces are trying drive out rebels who have established enclaves in the suburbs. While the government has lost control of large swaths of territory in the country's north and east, including parts of the northern city of Aleppo, the capital remains tightly secured.

Conditions in the city have worsened however, with prices for basic goods rising and fuel in short supply. U.S. officials said Thursday they believe Assad's sister and mother have left the country, suggesting that hardship has reached even the leadership's families.

As the fighting continued, France's foreign minister suggested that Assad's fall was not imminent -- a stark admission by a country that has been one of the most ardent supporters of the Syrian rebels.

Speaking in Paris, Laurent Fabius told reporters: "The solution that we hoped for -- that is to say, Bashar's fall, the rise of the opposition to power -- there are no recent signs that are as positive as that."

Meanwhile the Britain-based Syrian Observatory for Human Rights reported bomb attacks and clashes in a number of Damascus suburbs, saying at least 13 people were killed. The group, which relies on a network of contacts inside Syria, said fighter jets bombed the southwestern suburbs of Daraya and Moadamiyeh, where rebels have been fighting regime forces for weeks.

Because of its strategic location near a military airport, Syrian troops have been pounding rebel positions in Daraya for weeks. Earlier this month, the government claimed its troops had regained control of much of the district.

Activists posted a video of the Daraya fighting online that showed artillery shells slamming into concrete buildings, sending plumes of thick, gray smoke into the sky.

Daraya is flanked by the districts of Mazzeh, home to the military air base, and Kfar Sousseh, where the government headquarters, the General Security intelligence agency's head office and the Interior Ministry are located.

The Observatory also reported heavy fighting near Damascus International Airport and said the regime was shelling the town of Aqraba along the airport road.

State-run news agency SANA said troops have been battling rebels in the oil-rich province of al-Hasaka in the country's northeast, killing and wounding several "terrorists" -- the term the government and state media use to refer to rebels.

Also in the north, SANA said terrorists shot and killed a math teacher, Nabih Jamil al-Saad, on Wednesday near his home in the town of Hmaida in Raqqa province. A day earlier, rebels killed Mamdouh Abudllah Bin Abd Dibeh, a cardiologist, in front of his clinic in Sheik Mheddin area of Damascus, SANA said.

It was not clear if either the teacher or the doctor had ties to the regime. Rebels have targeted government officials, civil workers and prominent personalities, such as actors, who are known Assad supporters.

In a separate report, SANA said many residents of the central town of Salamiya in Hama province took part in a funeral procession for those killed in a car bomb explosion late Monday. The Observatory said earlier that at least 42 people were killed in an attack targeting the headquarters of a pro-government militia. SANA did not say how many died.

In photographs published by the official news wire, dozens of men are seen standing in front of 11 caskets, wrapped into Syrian flags. Another photograph by SANA shows hundreds of men rallying at what the official news wire said was a funeral procession at Salamiya's al-Huriyeh square.

Also on Thursday, in what Syrian state TV said was a live broadcast, Assad was seen sitting cross-legged on the floor of the al-Afram mosque in Damascus during prayers marking Prophet Muhammad's birthday.

Assad's public appearances have become rare as the civil war has consumed the country. He last appeared on January 6 at the Damascus Opera House, where he vowed in a televised address to keep fighting.

The U.S. officials who spoke about Assad's family said they did not know where his mother, Anisa, was, although they thought his sister, Bushra, was in the United Arab Emirates. Bushra was married to Deputy Defense Minister Gen. Assef Shawkat, who was killed in a Damascus bomb attack in July that also killed three other top officials.

UAE officials have declined to comment on the issue, but have noted that Assad's sister lived previously in the UAE and suggested she could have valid residency documents.

All officials spoke on condition of anonymity because they were not authorized to speak to the media.

According to the United Nations, more than 60,000 people have been killed in the Syrian conflict, which began almost two years ago when opposition supporters took up arms to fight a brutal government crackdown on dissent.

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Associated Press writers Albert Aji in Damascus, Syria, Matthew Lee in Washington and Brian Murphy in Dubai contributed reporting.