BEIRUT (AFP) - An Islamist rebel group stormed Syria's largest prison on Friday, seizing two buildings in the complex near Damascus amid heavy fighting, the Syrian Observatory for Human Rights said.

"Jaish al-Islam entered Adra prison and seized two buildings in the women's section of the complex," said Observatory head Rami Abdel Rahman.

The rebels launched an offensive Wednesday on the regime-held complex, which lies in the Eastern Ghouta suburb of Damascus, capturing a hilltop before seizing part of the facility, he told AFP.

"Most of the prisoners there are activists, political figures, and human rights defenders who are against the regime" of President Bashar al-Assad, said Abdel Rahman.

At least 5,000 prisoners are being held at the facility, almost twice its capacity of about 3,000 prisoners, he added.

When Jaish al-Islam announced their upcoming offensive, security personnel in the women's section fled, taking the female detainees with them.

In an online statement, the rebel group said it had taken control of a hilltop and buildings around the prison as well.

Video footage published alongside the statement showed men firing heavy weapons beyond a wall of sandbags, while others darted between buildings carrying machine guns.

Corpses which the rebels claimed to be security forces who died trying to defend the prison could also be seen in the video.

Jaish al-Islam is the most powerful rebel group in the opposition stronghold of Eastern Ghouta, where Al-Qaeda's Syrian affiliate, Al-Nusra Front, is also present.

The prison in Adra has been targeted in the past by heavy rocket fire, and last month at least 11 people were killed and 56 wounded when rockets fell outside the prison, according to state media.

More than 240,000 people have been killed since Syria's war began in March 2011, and millions more have been forced to flee their homes.