"The terrorist Assad regime bears the most responsibility for all the crimes that happen in the homeland because it has opened the doors to those with different agendas to enter Syria and harm its stability so it can hide behind this and use it as an excuse to justify its crimes," the group said in a statement on its Facebook page.
U.S. State Department spokeswoman Victoria Nuland condemned the "indiscriminate violence against civilians."
U.N. Secretary-General Ban Ki-moon condemned "the series of bombings in populated areas in the Syrian capital Damascus today, which resulted in numerous deaths and injuries," and expressed condolences to the families of victims.
Russia's state-owned RIA Novosti news agency quoted a Russian Embassy official as saying its building had been damaged in the blast but no one was hurt.
Among those injured by flying glass was Nayef Hawatmeh, the leader of the Democratic Front for the Liberation of Palestine, a radical Damascus-based Palestinian group. He suffered cuts to his hands and face, according to an official at his office, which is about 500 yards from the bomb. Hawatmeh was treated at a hospital and released.
In a separate attack, Syrian state TV said mortar shells hit near the Syrian Army General Command but caused no casualties. The report said the building was empty because it was being repaired from a bombing last year.
The Observatory said two mortar rounds struck near the building but it did not report casualties. It also said two more shells landed in the upscale Malki neighborhood, causing no damage or casualties.
Another blast in the northeastern Barzeh neighborhood killed seven people, a security official said, speaking on condition of anonymity because he was not authorized to brief the media.
The Observatory, which relies on a network of activists inside Syria, said three separate car bombs exploded near different security facilities in Barzeh, followed by intense clashes between rebels and regime forces. It said 22 people were killed, 19 of them security officers.
State media also reported that security forces in Damascus had arrested a second, would-be suicide bomber driving a car full of explosives near the site of the Mazraa bombing.
On Wednesday, two mortar shells exploded next to a soccer stadium in Damascus, killing one player. A day earlier, two shells hit near one of Assad's three palaces in the city, with some damage reported.
In the southern town of Daraa, where Syria's uprising began nearly two years ago, the Observatory said 18 people were killed in an airstrike on a field hospital, included eight rebel fighters, three medics, one woman and a young girl.
A video posted online showed the dead and wounded being loaded into the backs of trucks. Some were bloody and had bandaged heads, while others were carried on stretchers.
The videos appeared to be authentic and corresponded with Associated Press reports of the events depicted.
The conflict began in March 2011 with political protests against the government, and has since evolved into a civil war between Assad's regime and hundreds of rebel groups seeking to topple it.
International diplomacy has failed to slow the fighting.
British Foreign Secretary William Hague said Thursday that his message to Assad is "it is time to go," and that the senseless killing must be brought to an end through a political process.
He also urged Assad to respond to a dialogue offer made recently by Syrian opposition chief Mouaz al-Khatib.
"A political agreement on a transition is the way forward in Syria to bring to an end this terrible and unacceptable loss of life," he said.
Al-Khatib has said he is open to talks with the regime as a way of removing it from power. The government has refused, insisting the talks should be without preconditions and inside the country.
The Syrian National Coalition met in Cairo on Thursday to try to firm up its position on whether to engage with the regime in talks. A final decision was expected Friday.
Lucas reported from Beirut. Associated Press writers Ben Hubbard and Zeina Karam in Beirut, Bradley Klapper in Washington and Edith Lederer at the United Nations contributed to this report.