People gather near a damaged site after an Israeli air strike on Iran's consulate in Damascus on Monday. Reuters

Israeli air strikes destroyed the Iranian embassy's consular annex in Damascus on Monday, Syrian and Iranian officials said, with a top Revolutionary Guard commander among seven members the force said were killed.

Israel said it would not comment on the attack, but Iranian officials vowed a stiff response, with fears of even further violence between Israel and Iran's allies amid the Gaza war.

Iran's Islamic Revolutionary Guard Corps named Brigadier General Mohammad Reza Zahedi and another high-ranking officer, Brigadier General Mohammad Hadi Haji Rahimi, as among seven of its members killed.

Britain-based war monitor the Syrian Observatory for Human Rights said 11 people, including several Guards members, were killed when "Israeli missiles... destroyed the building of an annex to the Iranian embassy".

The toll includes "eight Iranians, two Syrians and one Lebanese — all of them fighters, none of them civilians," Rami Abdel Rahman, who heads the Observatory with a network of sources in Syria, told the media.

This photo shows the rubble after an Israeli airstrike on Iran's consulate in Damascus, Syria, on Monday. Reuters

Iran's ambassador to Syria, Hossein Akbari, told Iranian state TV that the attack "was carried out by F-35 fighter jets" that fired six missiles at the building.

AFP reporters saw the annex building had caved in, and emergency services were searching for victims under the rubble as sirens wailed in the upscale Damascus district of Mazzeh.

Security personnel shielded the site where earth-moving equipment was brought in to clear debris and remove charred vehicles from the road as a crowd gathered to watch.

Syria's defence ministry said that "the attack destroyed the entire building, killing and injuring everyone inside, and work is underway to recover the bodies and rescue the wounded from under the rubble".

Agence France-Presse