Government troops also shelled residential areas in the cities of Hama and Homs, and the nearby town of Rastan, killing at least 10 people, while a soldier died in a raid on an army checkpoint in the south, opposition sources said.
The lightly armed rebel forces have been forced into retreat across the country in recent weeks, with the army using heavy armour to chase them from towns and cities, chalking up its latest victory in Deir al-Zor, which lies on the road to Iraq.
"Tanks entered residential neighbourhoods, especially in southeastern areas of Deir al-Zor. The Free Syrian Army pulled out to avoid a civilian massacre," a statement by the Deir al-Zor Revolution Committees Union said.
After failing to hold significant stretches of land, analysts say the rebels appear to be switiching to insurgency tactics, pointing to bloody car bomb attacks in two major Syrian cities at the weekend and the sabotage of a major rail link.
Assad, fighting for the survival of his family dynasty which has ruled Syria for more than four decades, faces growing pressure from foreign powers, including ally Russia, to grant daily ceasefires that would enable humanitarian missions.
His forces have been accused of torture and arbitrary executions while trying to put down the insurgency, but advocacy group the Human Rights Watch said on Tuesday the armed opposition was also guilty of serious offenses.
"The Syrian government's brutal tactics cannot justify abuses by armed opposition groups," said Sarah Leah Whitson, Middle East director at Human Rights Watch, citing cases of kidnapping, torture and cold-blooded killings.
In a fresh effort to form a united international front on the mounting crisis, France has circulated a Western-drafted statement for the U.N. Security Council deploring the turmoil and backing peace efforts by UN-Arab League envoy Kofi Annan.
Britain's UN envoy said he hoped the statement would be adopted on Tuesday.
Syrian opposition released an army general abducted in the Damascus suburb of Douma in return for prisoners and bodies of insurgents and civilians held by police, an opposition source familiar with the deal said on Tuesday.
"Naeem Khalil Odeh has been released in return for several prisoners and 14 bodies," the source said from Douma, referring to the general, adding that he had been seized last week.
The British-based Syrian Observatory for Human Rights, which has contacts throughout Syria, said army shelling had killed seven people in Homs early Tuesday, while a married couple and their child died in a mortar attack in nearby Rastan.
Homs became the epicentre of the year-long rebellion against Assad and has been repeatedly targeted by government troops, who are believed to have swept most rebel gunmen from the city.
There has also been fighting further to the north around Hama, and opposition sources said Syrian tanks had bombarded the city early Tuesday to try to dislodge Free Syrian Army rebels who had resumed operations there despite several army sweeps.
The Free Syria Army has proved little match for Assad's well-armed security apparatus, and experts said the opposition appeared to be changing tactics.
Car bomb attacks in the capital Damascus and second city Aleppo killed at least 30 over the weekend, while rebels also destroyed a railway bridge linking Damascus to Deraa, according to official Syrian media.
"The Syrian opposition prematurely tried to hold territory and take on the Syrian Army. This was a bad and costly mistake," said Joshua Landis, the head of Middle East Studies at the US University of Oklahoma.
"In the new phase of the battle that is shaping up to combat the Assad regime, opposition leaders are likely to champion new tactics of militancy and Islamization," he wrote on his blog Syria Comment.
Analysts have long warned that the uprising risks becoming a fullblown civil war, pitting Assad's minority Alawite sect against the Sunni Muslim majority, who make up some 75 percent of Syria's 23-million-strong population.
The United Nations says more than 8,000 people have died in 12 months of turmoil. The government says 2,000 members of the security forces have been killed by foreign-backed "terrorists".
Reports from Syria cannot be independently verified because authorities have barred access to rights groups and journalists.
Moscow and Beijing have twice vetoed UN Security Council resolutions that condemned Syria's yearlong assault on rebels.
The statement circulated by France at the Security Council would not be a formal resolution, which carries legal weight, but rather a "presidential statement", which is generally non-binding but still needs unanimous backing.
In a sign Moscow might be willing to put some pressure on Syria, Russia's foreign ministry issued a statement on Monday calling on both Damascus and the armed opposition to agree "without delay to daily humanitarian pauses".
Syria has previously resisted such a demand, saying the fighting can only end when the rebels lay down their arms.