The Syrian Observatory for Human Rights said 12 children were among those killed in the opposition-held Eastern Ghouta region outside Damascus, and an AFP photographer there described chaotic scenes.
In the capital, meanwhile, a barrage of at least 120 rockets and mortar rounds fired by rebel forces killed 10 people, among them a child.
The fire left usually busy streets of the city deserted and prompted Damascus University to close for the day, sending students home.
"Within minutes, our busy street was empty," a resident of Damascus' Baramkeh neighbourhood told AFP after the mortar fire began, adding that the head teacher of a local school had been forced to take her students to a shelter.
More From This Section
The middle class district of the capital is home to several university buildings, as well as the headquarters of state news agency SANA.
"If the terrorists think that by shelling Damascus they will ease the pressure on them, they are making a big mistake," a senior military official said, speaking on condition of anonymity.
"We will continue to hunt them down and destroy them."
Jaysh al-Islam leader Zahran Alloush had warned that Damascus would be considered a "military zone" during the bombardment, which follows a similar attack by the group on January 25 that killed six.
The government's response was swift and deadly, with more than 60 air strikes hitting areas across Eastern Ghouta, along with surface-to-surface missiles, the Observatory said.
"This is the worst day in Douma in four years," he said.
"The situation in the hospitals is very bad. There are shortages of everything."
He said medics had been wounded in the shelling and residents were hiding in basements.
Local field hospitals were overwhelmed by arrivals, some of whom lay on the floor to receive treatment.