The Abdullah Azzam Brigades said it had carried out the simultaneous bombings as retaliation for the Lebanese Shiite group Hezbollah's involvement in the Syrian war alongside President Bashar Assad's forces.
It was the latest in a string of deadly bombings targeting Hezbollah strongholds in Lebanon. The group is a staunch ally of Assad's government and its fighters have been instrumental in helping dislodge Syrian rebels from key areas near the border with Lebanon.
Rahmeh Abboud, a 20-year-old student, said she was in a passenger van when she heard the explosions. The driver immediately stopped the car and told everybody to get out.
"The explosions were very strong, the ground shook. I came here and it was like the world had turned upside down," she said.
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The Lebanese army said the attack was carried out by suicide bombers driving BMW and Mercedes cars.
The explosions went off near Iran's cultural centre and the Kuwaiti Embassy. Blast walls were set up in front of the Iranian cultural centre recently for fear of such attacks. The white building suffered serious damage from the outside.
The state-run National News Agency quoted the Iranian embassy as saying that there were no serious injuries among diplomats and workers there.
The Abdullah Azzam Brigades said on its Twitter account that the "invasion of the Iranian cultural centre" was in "retaliation for Iran's party fighting along the criminal regime in Syria." It was referring to Lebanon's militant Hezbollah group.
It said Hezbollah will not "enjoy security in Lebanon until the people of Syria feel secure."
Hezbollah legislator Ali Ammar, speaking from the site of the blasts, said the group "will not withdraw from a strategic battle that aims to foil plans to divide the region."
Iran is a major backer of Hezbollah and both are allies of Assad.
The explosions came few days after Prime Minister Tammam Salam formed a new cabinet after almost 11 months of paralysis. He said Wednesday that the attack is "a message by forces of terrorism to continue in their plan to spread death in Lebanon."
One of the deadliest attacks occurred in November when two suicide attackers blew themselves outside the Iranian Embassy in Beirut, killing 23 people and wounded dozens. That attack was claimed by the Abdullah Azzam Brigades.
The group's leader was captured by Lebanese authorities in December and died in custody later in the month.