In the north, clashes between rival rebel factions left nearly 50 gunmen dead in three days of fighting for control of neighborhoods in the city of Aleppo, an activist group said.
An 8-year-old girl was killed and 11 people were hurt in the blasts in the upscale Abu Roumaneh area of Damascus, the SANA news agency said. One shell fell near a school and the other on the roof of a building.
The girl was in her family car near the school when she was killed, said the Syrian Observatory for Human Rights, a Britain-based activist group monitoring the fighting.
The blasts damaged several cars and shattered nearby windows. One resident was seen sweeping debris on a sidewalk, near where twisted metal pieces from the wreckage had been heaped in a small pile.
The blasts struck some 300 meters (1,000 feet) away from the Four Seasons Hotel where the chemical weapons inspectors and U.N. staff are staying. A U.N. employee staying there said it did not appear that the hotel was affected by the twin explosions. The hotel remained open after the blasts, he said, speaking on condition of anonymity because he was not authorized to speak to reporters.
He said he heard the first explosion at about 11:15 a.m., followed by a second. Thick smoke rose from the area and ambulance sirens sounded shortly afterward.
Syrian rebels routinely fire mortar shells from the outskirts of Damascus at city neighborhoods controlled by forces loyal to President Bashar Assad. Last week, a similar attack reportedly killed eight people.
Inspectors from the Organization for the Prohibition of Chemical Weapons and U.N. staff have been in Syria for the past two weeks to destroy the country's chemical weapons stockpile. The watchdog agency working to eliminate chemical weapons around the world won the Nobel Peace Prize on Friday in a powerful endorsement of its Syria mission.
The OPCW inspectors have so far visited three sites linked to Syria's chemical weapons program, though the agency has not provided details. On Saturday, before the mortar attack, a convoy of U.N. cars left the Four Seasons, but its destination was not known.
The inspectors' mission in Syria is unprecedented because of a tight timetable—they are to get the job done by mid-2014—and because they are operating in the midst of a civil war.
They are to inspect more than 20 sites, some close to front lines crisscrossing the country.
Earlier this week, Syrian warplanes twice bombed the rebel-held town of Safira, just a few kilometers (miles) from a large military complex believed to house an underground chemical weapons production facility.
Another mortar attack Saturday in the regime-held Damascus suburb of Jaramana left two people dead and several others wounded, according to the Observatory.
SANA said that the Ministry of Social Affairs and the Syrian Arab Red Crescent evacuated Saturday nearly 2,000 women and children from the rebel-held Damascus suburb of Moadamiyeh where people have complained about lack of food. SANA gave no further details.
The Syrian conflict erupted in March 2011 as a popular uprising against Assad that quickly escalated into civil war. More than 100,000 people have been killed since then and millions of Syrians have been displaced.
In the northern city of Aleppo, Syria's largest, 44 fighters were killed in three days of clashes between al-Qaida's Islamic State of Iraq and the Levant and a rival group formerly known as Ghurabaa al-Sham. The Observatory said 14 of the dead belonged to ISIL, which was able to control three neighborhoods in Aleppo.
Rebel groups have become increasingly fractured, with Islamic extremists, including those linked to al-Qaida, assuming prominent roles in battle.
In an audio message Friday, the leader of al-Qaida urged jihadis in Syria to unite, an appeal likely aimed at rival affiliates of his terror network operating in the country.
Ayman al-Zawahri said fighters must "rise above organizational loyalties and party partisanship" and unite behind the goal of setting up an Islamic state. He suggested he will not impose unity, saying that "what you agree upon will also be our choice."
Two al-Qaida-linked groups have emerged—Jabhat al-Nusra and ISIL. The first is commanded by a Syrian, the second by an Iraqi, but both are believed to be loyal to al-Zawahri.
Al-Zawahri also urged Syrian regime opponents not to cut deals with Westerns and secular groups.
Associated Press writers Diaa Hadid and Bassem Mroue in Beirut and Maamoun Youssef in Cairo contributed to this report.