In the past weeks, anti-regime activists say about 150 people have been killed a day in fighting. Since the uprising against Assad began in March 2011, they say 35,000 have died.
Tuesday's airstrikes came a day after what activists called the heaviest and most widespread bombing campaign nationwide, on what was to be the final day of an internationally sanctioned truce that never took hold.
The death toll for what was supposed to be a four-day cease-fire ending Monday exceeded 500.
Activists speculated that the government's heavy reliance on air power reflected its inability to roll back rebel gains, especially in the north of the country near the border with Turkey, where rebels have control of swathes of territory.
The international community remains at a loss about how to stop the Syria violence. The U.S. and other Western and Arab nations have called on Assad to step down, while Russia, China and Iran continue to back him.
In the latest fighting after nightfall Tuesday, the Britain-based Syrian Observatory for Human Rights said 18 civilians were killed in an airstrike and tank fire Tuesday in the Hajariyeh neighborhood in the suburb of Douma, northeast of Damascus.
The dead included four women and five children, the group said, adding that the toll could rise as residents were still searching through the rubble.
Five rebel fighters were also killed in clashes with regime forces elsewhere in Douma, the group said.
Amateur videos posted online showed a deep, rubble-filled crater in the middle of what appeared to be a poor neighborhood, with many walls collapsed in the blast.
Men were seen chanting "God is great!" while pulling a mangled body from the rubble in one video. They used their hands to dig through cinder blocks and cement dust in another to uncover another dead body.
In yet another video, a man standing in the destruction yells at the camera, "These are the accomplishments of Lakhdar Brahimi," referring to the international envoy who proposed the recent, failed cease-fire.
Regime airstrikes also collapsed buildings in the rebel-held northern city of Maaret al-Numan, which straddles a key supply route from the capital to Aleppo, Syria's largest city and a main front in the civil war.
Assad's regime has been hammering away at Maaret al-Numan, 80 kilometers (50 miles) southwest of Aleppo, with heavy airstrikes since it fell to rebels on Oct. 10.
One amateur video purporting to show the aftermath of an airstrike on Tuesday showed a man holding up the dead body of a small girl in a red and white shirt and baby blue pants. Other videos showed men carrying bloodied women and children from destroyed buildings.
The Observatory said the day's airstrikes on the city killed at least seven people, four of them children.
One video showed the bodies of three girls wrapped in white shrouds. Nearby, a man dripped water on the face of a dead older man with a white beard, saying: "Go to heaven, dad. May God take revenge."
The Observatory said at least one rebel fighter was also killed in clashes south of the city, and regime forces were trying to bring in reinforcements from further south.
Activist claims and videos could not be independently verified because of restrictions on reporting in Syria, but the videos appeared genuine and corresponded with other Associated Press reporting on the events depicted.
Violence also flared elsewhere in and around Damascus. The Observatory said missiles fired from a fighter jet struck the capital's Jobar neighborhood a rare hit in the capital's municipal area. Most of the fighting around Damascus for the past few months has been in suburbs and outskirts, where rebels have managed to challenge the regime.
Syria's state news agency said an "armed terrorist group" assassinated a high-ranking air force general. Maj. Gen. Abdullah Mahmoud al-Khalidi was gunned down while getting out of his car in the mostly Kurdish neighborhood of Rukn Eddine in Damascus.
The government views the rebels as terrorists and accuses them of being foot soldiers in a foreign plot to destroy Syria.
In Turkey, Foreign Minister Ahmet Davutoglu expressed "great sadness" that the cease-fire had failed and said government was done talking to Assad's regime.
"Unfortunately the attacks continued, and the Syrian people spent the holidays suffering great pain," Davutoglu told reporters in Ankara. "There would be no meaning to forging a dialogue with a regime that pressed ahead with such a massacre even during the holidays."