A second blew up a vehicle outside a nearby military intelligence building.
State television showed pictures of a huge crater at one of the bomb sites and pools of blood on surrounding pavements.
Bystanders were seen carrying away charred and mangled bodies wrapped in makeshift shrouds.
"On the first day after the arrival of the Arab observers, this is the gift we get from the terrorists and Al-Qaeda but we are going to do all we can to facilitate the Arab League mission," Deputy Foreign Minister Faisal Meqdad told reporters at one of the bomb sites.
Asked to comment on suggestions that the bombings had been engineered by the regime itself, Meqdad shot back: "anyone who makes such allegations is a criminal."
While not specifically rejecting Syria's account of what happened, France accused the regime of trying to hide its brutal tactics from foreign observers.
"We still don't have any details on the origin of these attacks," foreign ministry spokesman Bernard Valero said when asked whether Paris shares suspicions that the regime might have staged the bombings.
However, Valero said France was more generally concerned that Syria had been carrying out actions for several days "to mask the reality of the repression, notably by transferring political prisoners to secret jails.
"Bashar al-Assad is wrong if he thinks he can once again trick the international community by play acting, lies and procrastination," he said.
State Department spokesman Mark Toner said the "United States condemns in the strongest terms the bombings today in Damascus," adding that there is "no justification for terrorism of any kind and we condemn these acts wherever they occur."
He also said it was "crucial that today's attack not impede the critical work of the Arab League monitoring mission to document and deter human rights abuses with the goal of protecting civilians."
Lebanese President Michel Sleiman condemned the blasts as "terrorist attacks" and said they were aimed at disrupting the Arab League's efforts to resolve the crisis.
Syria's deputy foreign minister was accompanied to the bomb site by Arab League Assistant Secretary General Samir Seif al-Yazal, head of the observer mission's advance team, which arrived on Thursday.
"What has happened is regrettable but the important thing is that everyone stay calm," Yazal told reporters.
"We are going to press on with our work. We have started today, and tomorrow (Saturday) we will meet (Foreign Minister) Walid Muallem."
Yazal's nine-strong team is making the necessary logistical arrangements for the arrival of a first 30 observers on Sunday. The mission will eventually number between 150 and 200.
The mission is part of an Arab plan endorsed by Syria on November 2 that also calls for the withdrawal of the military from towns and residential districts, a halt to violence against civilians and the release of detainees.
Muallem has said he expects the Arab observers to vindicate his government's contention that the unrest is the work of "armed terrorists," not overwhelmingly peaceful protesters as maintained by Western governments and human rights watchdogs.
State news agency SANA said Thursday that more than 2,000 security force personnel had been killed in attacks by armed rebels.
But opposition leaders have charged that Syria's agreement to the mission after weeks of prevarication was a mere "ploy" to head off a threat by the Arab League to go to the UN Security Council over a crackdown, which the world body says has left more than 5,000 people dead since March.
There was no let-up in the bloodshed on Friday with human rights activists reporting at least 14 civilians killed by security force fire.
Eight were killed in Homs, two in Hama, two in the Damascus suburb of Douma, one in Daraa and one in Idlib.
At the United Nations, meanwhile, tensions over Syria remained high, with Western nations accusing Assad-ally Moscow of trying to divert attention from the crisis by pressing for an enquiry into NATO's involvement in the recent Libyan war.
And in Ottawa, Canada's Foreign Affairs Minister John Baird announced the freezing of assets of more Syrians loyal to Assad's regime, as well as a beefed up trade ban.