The authenticity of the video could not be confirmed. It showed a finger pressing a button on a white box with wires, and then images two missiles or rockets flying up into the air. The video did not show any impact with a plane. Instead, it cut to footage of people in street clothes walking through a plane's wreckage burning on the ground.
It was not immediately possible to determine if the wreckage was that of the British C-130 Hercules that crashed Sunday about 25 miles north of Baghdad.
In London, officials at the Foreign Office said they were aware of the reported video, but offered no further comment.
A spokesman for al-Jazeera said the television station received the video from a group that called itself "the Green Brigade," part of the "the 1920 Revolution Brigade, a military wing of the National Islamic Resistance in Iraq."
Earlier Monday, a different group, Ansar al-Islam, claimed in a Web statement that its fighters shot down the flight with a missile. That group provided no evidence of the claim.
A spokesman for Britain's Ministry of Defense said earlier he could not confirm Ansar's claim or that the plane was downed by insurgent fire. He said experts were at the site trying to determine the crash's cause.
British Defense Secretary Geoff Hoon said nine British air force personnel and one soldier were missing and believed killed in the crash, which would make it the deadliest single incident for British forces in Iraq since the war began in March 2003.
An insurgent group called "The 1920 Revolution Brigade of the National Islamic Resistance in Iraq" first emerged in Iraq's Sunni Triangle in July of 2003. But the Green Brigade of that group has not been heard of before.