The unidentified witness said just two paratroopers - identified as Lance Corporal F and Soldier G - were probably responsible for eight or ten of the deaths of the 13 unarmed men.
The Tribunal is now sitting in London, having moved from Derry.
The move follows court action in which the witnesses had argued they could be targeted by dissident Republicans if they had to travel to the North.
The former solider, known only as Soldier 027, has been giving his evidence to the Saville Inquiry from behind a curtain screening him from the media and the public gallery.
The man was a radio operator with the Parachute Regiment in Derry on Bloody Sunday in January 1972.
He has been describing how the soldiers had been psyched up before they arrived because they believed they were going to be attacked by the IRA.
Counsel to the inquiry, Christopher Clarke QC, has been taking him through his written statement to the inquiry line by line.
In that statement, Soldier 027 identifies two colleagues - Lance Corporal F and Soldier G - as firing without hesitation or justification in Rossville Street and in the Glenfadda Park area.
He says those two men alone were probably responsible for eight or ten of the thirteen people killed on the day.
Soldier 027 says he neither fired his own weapon nor did he see any civilians with weapons. Several other former soldiers, due to give evidence in London, are expected to strongly contest his version of events.
