Syria's army on Saturday pressed a fierce assault launched four days ago against rebel areas in northern and eastern Damascus, killing three children with mortar fire, a monitoring group said.
In northern Syria, rebels said they had begun a new assault on regime-held neighbourhoods of the country's second city, Aleppo.
"The district of Qaboon in (northeastern) Damascus is being intensely shelled by regime forces," the Syrian Observatory for Human Rights reported.
Rebels were resisting the onslaught, battling troops loyal to President Bashar al-Assad on the edges of Qaboon, it said.
Afternoon shelling in Qaboon killed or wounded several people, after a bus filled with passengers was hit, the Britain-based group said.
Overnight mortar fire targeting Qaboon had already killed three children from one family, it added.
Nearby, as fighting raged in the flashpoint district of Barzeh, rebels fired rockets at a police academy in the neighbourhood, said the watchdog.
It also said two mortar rounds hit Abbasiyeen Square in the northeast of the capital, one of Damascus's main landmarks.
Several people were wounded in the attack, the group said.
Over the past fortnight, the army has dramatically boosted efforts to crush the anti-Assad insurgency in and around Damascus.
Meanwhile in Aleppo, large swathes of which are under rebel control, the main rebel Free Syrian Army (FSA) command announced in an online statement the launch of "a battle to liberate several western districts".
Activists said fierce fighting raged in the regime-held New Aleppo district in the west.
Rebels launched their first major assault on Aleppo on July 20 last year. Despite fierce fighting since, there is now a stand-off in the city.
The latest assault is being staged by 13 rebel groups, including the powerful Liwa al-Tawhid and the Farouq Battalion, the FSA statement said.
Saturday's fighting was heaviest in the Rashidin area of New Aleppo, an activist in the city told AFP via the Internet.
"A fire broke out in a (military) research centre in New Aleppo after the revolutionary brigades used mortars to shell it," said the activist identifying himself as Mohammad, adding that the rebels were advancing on Rashidin.
The rebels "are focusing on hitting military targets" in the area, he said.
Mohammad said Aleppo's western districts are key because the army has been shelling rebel areas from there.
The escalation comes two weeks after pro-regime media said the army was ready to assault Aleppo.
"The regime spent the past weeks trying to prove to world public opinion that it is in control of the course of Syria's war -- but this is not true," said Aleppo-based activist Abu Omar.
"The regime's only battle here is a media battle."
The developments come as the military in the central province of Homs also pushed on with its bid to end the insurgency there, said the Observatory.