Rebel fighters have stormed an army post in Douma, killing six soldiers, while intense shelling by government forces sent residents of the Damascus suburb fleeing in panic, a rights group and activists said.
Other rebel-held bastions in and around Damascus were also bombarded at dawn on Tuesday as the government said it was close to crushing the last pockets of resistance in the capital.
The violence came hours after UN chief Ban Ki-moon urged Damascus to show compassion to its people and Walid al-Moualem, the Syrian foreign minister, said a political solution was still possible if the West and Gulf states halted support for the rebels.
The Syrian Observatory for Human Rights, a UK-based anti-government rights group, said that at least two civilians died when Douma, in the capital's northeast, was rocked by shelling following the deadly raid by the rebels during the night on a medical centre there that has now been taken over by the military.
"The army had transformed the centre into a barracks and snipers were positioned there," Observatory director Rami Abdel Rahman said.
Troops loyal to President Bashar al-Assad also targeted a string of rebel strongholds in towns and suburbs outside the capital at dawn, including in Babila, Hosh al-Arab, Saqba and Zabadani, the Observatory said.
The Local Co-ordination Committees, an anti-government activist network, reported that more than 100 shells fell on Zabadani, once a resort destination known for its mild weather and scenic views just northwest of the capital but now devastated by the civil war ravaging Syria.
Elsewhere in Damascus province, the town of Yabroud came under fierce artillery fire, the LCC said.
'End of security operations'
The official daily Al-Baath on Tuesday said that the "end of security operations throughout Damascus province" was approaching.
Government forces "have destroyed many weapons caches and seized large quantities of ammunition and equipment ... which indicates that the end of security operations throughout Damascus province is approaching," the newspaper said.
Rebels on July 18 carried out a massive bombing on a security complex in Damascus, killing Assad's brother-in-law, the defence minister and a general.
Since then regime forces have pushed the rebels to the outskirts of the capital but have lost control of several border crossings and are battling to retake Syria's second city of Aleppo, which has been the focal point of the conflict since mid-July.
The Observatory said that Aleppo's northeast district of Hanano City again came under bombardment on Tuesday, a day after 19 civilians were killed in shelling there and in other districts.
Fighting between troops and rebels also flared in the Arkoub, Sakhur, Sheikh Khodr and Sheikh Faris districts as well as along Suleiman al-Halabi street in the city centre, the watchdog said.
Rebels and loyalist troops on Monday clashed in the centuries-old UNESCO-listed Aleppo souk, days after it was ravaged by a fire sparked by earlier fighting.
On the political front, Ban said after a meeting with Syria's Muallem at UN headquarters in New York that it was time for Damascus to lower the scale of its offensive against the uprising.
In-depth coverage of escalating violence across Syria
"He stressed that it was the Syrian people who were being killed every day and appealed to the government of Syria to show compassion to its own people," a spokesperson for the UN secretary-general said.
Moualem, meanwhile, addressing the UN General Assembly, said France, Qatar, Saudi Arabia, Turkey and the United States "clearly induce and support terrorism in Syria with money, weapons and foreign fighters".
Assad was open to reforms if the violence stopped, the foreign minister said. "We still believe in a political solution as an essential way out of the crisis."
For this to happen, he said UN members should press for an end to the "arming, financing, harbouring and training of terrorist groups".
Ali Akbar Salehi, the Iranian foreign minister, also in New York for the UN General Assembly, said Tehran could not support any country, including ally Syria, that used such weapons.