The Britain-based Syrian Observatory for Human Rights that 24 of the dead, including all eight children, were killed by government air and artillery strikes in the eastern Ghouta district on Sunday. The rest of the casualties were in towns and villages outside the capital, the Observatory said, and included 13 rebels killed in clashes.
Activists said the bombardments were some of the heaviest in the Damascus region since the government launched a series of offensives there in November.
On Monday, Syrian fighter jets carried out fresh airstrikes on the strategic suburb of Daraya, from which opposition fighters have tried to storm Damascus, the seat of Assad's power.
Daraya is close to a number of strategic facilities. The suburb is flanked by the key districts of Mazzeh, home to a military air base, and Kfar Sousseh, where the government headquarters, the General Security intelligence agency head office and the Interior Ministry are located. Last week, the government said it has regained control over more than half of the suburb.
The regime's current push in Damascus comes a week after Assad dismissed international calls to relinquish power and vowed to continue fighting rebels, whom he characterized as Islamic extremists out to destroy Syria.
The speech was condemned by the U.S. and its Western and Gulf Arab allies, while Assad's backers in Russia and Iran said his proposal should be considered.
Syria's opposition rejected the proposal.
Those fighting to topple the regime, including rebels on the ground, have repeatedly said they will accept nothing less than the president's departure, dismissing any kind of settlement that leaves him in the picture.
Russia's Foreign Minister Sergey Lavrov criticized Western demands that Assad steps down. While acknowledging that the initiatives to talk to the opposition, "probably don't go far enough," Lavrov called on the opposition to come up with their plan to end the bloodshed.
"President Assad put forth initiatives which are aimed at inviting all opposition members to a dialogue," Lavrov said Sunday during a visit to Ukraine.
"If I were in the opposition's place, I would put forth my own ideas in response on how to establish a dialogue," Lavrov said.