Aleppo-based activist Mohammad Saeed said Wednesday's blasts went off minutes apart and appeared to be car bombs and were followed by clashes and heavy gunfire.
"The area is heavily fortified by security and the presence of shabiha," he said, referring to pro-Assad gunmen. "It makes you wonder how car bombs could reach there."
Syrian state TV said three suicide bombers detonated cars packed with explosives in Saadallah al-Jabri Square, near an officers' club. The square holds symbolic importance for residents because it is named after a Syrian independence fighter who resisted French occupation.
Activists and Syrian state media said a fourth car bomb went off a few hundred meters (yards) away in the Bab Jnein area near the Old City. It was not immediately clear how many casualties there were from that blast.
The Syrian Observatory for Human Rights said mortars also targeted the nearby political security department around the same time of the bombings.
Syria's Interior Ministry vowed to "track down the perpetrators anywhere." The speaker of the Syrian parliament, Mohammad Jihad al-Lahham, told the assembly that he condemns "the countries that conspire against Syria and stand behind the terrorists."
Israel also is concerned that fighting from Syria's civil war could spill across the border. Last month, mortar shells exploded in Israeli-controlled territory. Nobody was hurt and Israel said the shells were misfired.
On Wednesday, the Israeli military said dozens of armed men have gathered on the Syrian side of the frontier in the Israel-controlled Golan Heights. Authorities closed a tourist site there in response.
An Israeli spokesman said it was unclear what the armed Syrians were doing. He said there was no violence, and a tour group left Mount Hermon without incident. The army was watching the area. He spoke on condition of anonymity under military rules.
Israel captured the Golan Heights from Syria in the 1967 Mideast war. It later annexed the strategic territory in a move that is not recognized internationally.
Torchia reported from Istanbul Associated Press writers Zeina Karam in Beirut; Manu Brabo in Aleppo, Syria; Albert Aji in Damascus, Syria; Don Melvin in Brussels; and Bradley Klapper in Washington contributed to this report.
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