Al-Jazeera said car bombs were used in the attack and that heavy exchanges of gunfire were continuing late into the night.
Al-Arabiya quoted a witness as saying over 15 explosions were heard.
Syria has been on the US State Department's list of terror-sponsoring nations for its support of anti-Israeli groups like Hamas and Hezbollah. But it says the anti-Israeli groups are not terrorist and that it has an interest in fighting Islamic extremist groups like al-Qaeda.
Syria is under intense pressure, particularly from the US, to crack down on militants in the country who are anti-Israeli or purportedly entering neighbouring Iraq to fight US soldiers.
Neighbouring Jordan said several suspected terrorists entered the country from Syria last month in a foiled plot to attack targets including the US embassy, the prime minister's office and the secret service agency.
Syria denied this, saying it is trying to stop militants crossing from its territory into Iraq.
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http://www.capetimes.co.za/index.php?fSectionId=272&fArticleId=417679Syria's Assad Sees 'Legitimate Resistance' in Iraq
"Certainly, what has happened on the popular level gives legitimacy to the resistance and shows that the major part of what is happening is resistance," Assad said in comments aired on Arabic satellite channel Al Jazeera.
"You are talking now about resistance which is against the occupation forces," Assad said. Asked if the resistance was legitimate, he said: "Well, of course, it's understood that way."
The United States has accused Syria of sheltering "terrorists" and not doing enough to stop foreign fighters infiltrating from its territory into neighboring Iraq.
Syria says it has done its utmost to control the border and has helped the United States in its "war against terror."
Parts of the interview were shown by the Qatar-based channel which Washington has accused of inflaming an anti-U.S. revolt.
Al Jazeera said the interview took place before rare violence hit the Syrian capital Damascus Tuesday when an armed group set off a bomb in the tightly controlled diplomatic quarter and four people died in ensuing gunbattles.
http://www.reuters.com/newsArticle.jhtml?type=worldNews&storyID=4969790Possible culprits
The BBC's Middle East analyst Roger Hardy says there are three possible culprits for Tuesday night's attack.
They might have been members of a resurgent Muslim Brotherhood, the pan-Arab outfit that spearheaded the Islamist revolt two decades ago.
They might be part of Syria's Kurdish minority, which was involved in street clashes in March.
Or finally, they could be agents of al-Qaeda - though this seems doubtful given the Syrian government's apparent disdain for US policies in the region.
Syria alert after mystery attack