Troops attacked the town of Daraya near Damascus, the scene of the worst massacre in the 20-month conflict, where more than 500 people were killed in late August, according to monitors.
"Regime forces are attempting to break into Daraya," said the Local Coordination Committees, a network of activists on the ground.
An official quoted by state media said the assault on Daraya "led to the elimination of a number of the most dangerous terrorist snipers of Al-Qaeda who were holed up in the homes of displaced residents."
In the central province of Homs, the Observatory and activists reported fierce bombardment of the rebel-held towns of Qusayr and Rastan, which the army has been trying for months to retake.
In the north, insurgents went on the offensive, attacking troops guarding the strategic Tishrin dam, located on the Euphrates River between Aleppo and Raqa provinces.
The rebels have surrounded the area, about 10 kilometres (six miles) from the town of Manbij, local resident Abu Mohammed told AFP.
Opposition fighters already control one of the main routes to Raqa, and the Tishrin dam would give them a second passage, connecting a wide expanse of territory between the two provinces, both of which border Turkey.
In Aleppo city, the commercial capital where fighting has reached stalemate after five months of deadly urban combat, clashes broke out near an air force intelligence building, the Britain-based Observatory said.
In Hasakeh province, northwest Syria, Ras al-Ain has seen its fiercest violence since the town near the Turkish border was captured by rebels two weeks ago, a resident told AFP.
"There are so few people, most have left. There is no electricity, no water and no mobile coverage," said Ali, a farmer in his 40s, who fled with his family on Saturday.
Hundreds of fighters loyal to the Kurdish Democratic Union Party (PYD) -- which has close ties to Turkey's rebel Kurdistan Workers' Party (PKK) -- have been locked in fierce battles with fighters of the jihadist Al-Nusra Front and allied Ghuraba al-Sham group in Ras al-Ain in recent days.
The Observatory, which relies on a network of activists, lawyers and medics, later reported that clashes had died down after the two parties managed to strike an agreement.
On the diplomatic front, influential Iranian parliament speaker Ali Larijani met Turkish Prime Minister Recep Tayyip Erdogan behind closed doors in Istanbul for two hours, Turkish news agency Anatolia reported, without providing details.
Larijani is on a regional tour, having already been to Syria and also planning to visit Lebanon.
Iran is a close ally of the Syrian regime, and just Friday said Turkey's request to site Patriot missiles on its border with Syria only "complicates" the conflict in the Arab country.
"Not only does it not help resolve the situation in Syria but it will also aggravate and complicate the situation," foreign ministry spokesman Ramin Mehmanparast said, quoted on state television.
"The insistence (of certain countries) to resolve the Syrian crisis through military means is the main cause of tensions and threats in the region," he said.
Turkey turned to its NATO partners earlier this week to request the deployment of surface-to-air Patriot missiles to protect its troubled border with Syria.