Fresh fighting has been reported around Syria's capital, Damascus, and in the northern city of Aleppo, where rebels are trying to secure their positions.
Most areas of Aleppo where rebels are entrenched have been bombarded by government forces and clashes have been reported in several districts.
The violence comes after a UN General Assembly vote to criticise the Security Council for failing to act on Syria.
The UN also condemned the Syrian government for its use of violence.
The focus of the fighting is also on the southern edge of Damascus where shelling and gunfire were reported from the Tadamon quarter, despite it having been earlier stormed by government forces, says the BBC's Jim Muir, reporting from Beirut.
Shooting and explosions were also being heard in some central parts of the capital, and activists reported clashes too on the western side of the city, in and around Dumar.
Video footage posted by activists showed a military jet flying over what they said was the rebel-held quarter of Salah al-Din in Aleppo followed by a loud explosion.
Activists reported clashes in several areas too, including around the officers' club and a political security headquarters.
But the regime has yet to unleash a concerted offensive to drive rebels out, though UN officials believe it is building up its forces for just such a campaign to regain control of a city it can't afford to lose, our correspondent adds.
Earlier, Russia and China condemned the UN resolution passed on Friday, saying that it undermined peace efforts.
Moscow's UN envoy, Vitaly Churkin, told reporters the resolution was one-sided and supported the armed opposition.
Western nations praised the resolution, which passed by 133 votes to 12 with 31 abstentions.
It criticises both the UN's own Security Council and the government of Syrian President Bashar al-Assad.
The assembly debated the resolution, which was proposed by Saudi Arabia, shortly after the resignation of UN-Arab League envoy Kofi Annan and the failure of his six-point peace plan.
Activists say more than 20,000 people - mostly civilians - have died in 17 months of unrest.