criminal police headquarters in the Duwar al-Jamarek area and air force intelligence offices in Al-Qasaa district, state television said.
"Twenty-seven people, mostly civilians, were killed and 97 others wounded in the two explosions," health minister Wael al-Halaqi said on Syria News, another official channel, as angry residents vented their fury at Arab supporters of anti-regime activists.
"According to our initial information, they were car bombs," state television said.
The broadcaster ran footage of a charred body inside the mangled remains of a smouldering vehicle in Duwar al-Jamarek. "First pictures of the body of one of the terrorists who targeted Damascus today," a message on the screen read.
The front of a multi-storey building was gutted by the impact of the other blast and several cars destroyed. The television broadcast images of wrecked apartments and blood-splattered streets.
An anti-regime activist in Damascus, Abu Muhannad al-Mazzi, told AFP the first blast struck at 7:30 am (0530 GMT). "A few minutes later, the second explosion, more powerful, rang out," he said.
The television showed an elderly woman being carried to an ambulance in her nightdress, while a wounded man, head bandaged and neck in a brace, was shown in hospital in his pyjamas and dressing gown.
Commentators on state television blamed Qatar and Saudi Arabia, the fiercest Arab critics of President Bashar al-Assad over his regime's deadly crackdown on dissent since last March, which have both called for rebels to be armed.
They carried "political, judicial and religious responsibility," one charged.
"Saudi Arabia is sending us terrorists," a witness said on television. "These are the friends ... of the Istanbul council," said another, referring to the opposition Syrian National Council set up in the Turkish city last August.
A spate of bombings have hit Syria's big cities in recent months amid growing concerns that Al-Qaeda has taken advantage of the year-old uprising against Assad to shift its focus of operations from neighbouring Iraq.
Twin bombs hit security services bases in the capital killing 44 people on December 23, with state media pointing the finger at Al-Qaeda. Rebels accused the regime of having stage-managed the attacks.
On Friday, UN-Arab League peace envoy Annan warned of a regional "escalation" of the deadly conflict in Syria and urged the UN Security Council to close ranks to put pressure on Assad.
The former UN chief, who met Assad in Damascus last weekend, has ordered a team of UN experts to Syria, on a trip starting on Sunday, to discuss a possible ceasefire and international monitoring mission, his spokesman said.
"We tend to focus on Syria, but any miscalculation that leads to major escalation will have impact in the region which would be extremely difficult to manage," he told reporters in Geneva, according to an official transcript.
Annan told the Security Council via videoconference that he has had a "disappointing" response from Assad so far to his proposals, diplomats at the meeting said.
The Security Council has been unable to pass a resolution condemning the violence. Russia and China have twice used their powers as permanent members to block resolutions which they said were unbalanced.
Syria's foreign ministry said the country would cooperate with Annan and at the same time pursue its crackdown on "armed terrorist gangs," which it holds responsible for the year of bloodshed.
The government is "determined to protect its citizens by disarming the terrorists and continues to search for a peaceful solution to the crisis," it said in a letter to the United Nations, reported by state news agency SANA.
Thousands of anti-government protesters called Friday for foreign military intervention to bring down Assad. The Syrian Observatory said at least 15 people were killed around the country.
A large crowd also took part in a rare demonstration in Al-Raqqa, a city in northeast Syria, as seen in a video posted on the Internet by activists.
"The people want military intervention, the Free Syrian Army to be armed, and the fall of the regime," several thousand demonstrators chanted in Syria's second-largest city Aleppo, an activist at the scene told AFP by telephone.
The Observatory said unidentified assailants killed two policemen and wounded three in Aleppo province on Saturday.
Huge rallies in support of Assad were held in Damascus and other major cities on Thursday to mark the first anniversary of the uprising that monitors say has cost more than 9,100 lives in 12 months.
Apart from the mission of Annan's technical team, the United Nations and Organisation of Islamic Cooperation are also to send experts to Damascus this weekend on a Syrian government-led humanitarian mission.
The United Nations estimates more than 30,000 Syrians have fled to neighbouring states and another 200,000 are displaced within Syria.