A statement from the air base said its personnel wanted to fight extremists, echoing the rhetoric of General Khalifa Haftar.
"The Tobruk air force base will join...the army under the command of General Khalifa Qassim Haftar," the statement said.
Staff at the air base confirmed its authenticity.
Heavily-armed gunmen apparently loyal to Haftar had stormed parliament on Sunday demanding it be suspended and power handed over to a 60-member body that is rewriting Libya's constitution.
The Tobruk air base development was significant as it was not clear how much backing Haftar's men had within Libya's nascent regular armed forces and the powerful brigades of former rebels who had toppled the former dictator Muammar Gaddafi in 2011.
Haftar, once a Gaddafi ally, turned against him over a 1980s war in Chad.
Haftar's forces attacked militants in the eastern city of Benghazi on Friday. More than 70 people were killed.
Tripoli was quiet on Monday with most people staying indoors after fighting raged across the capital on Sunday. Two people were killed in that violence.
The international airport was open though some flights were cancelled as travelers could not easily reach it. But authorities extended the closure of Benghazi airport for another week because of the unrest, the airport director said. It was attacked with rockets overnight.
RA/NJF