"I saw the green lorry in front of me stop and then reverse so I stopped too, locked the truck and ran," Idriss said.
Davide Capello, a former goalkeeper for Italian football club Cagliari Calcio, said his vehicle went down with the bridge and he felt "incredibly lucky" to be alive.
"I remember that the road was collapsing, I was passing through and I heard a deafening sound and I saw the road going down and I was going down with it and I thought the worse," Capello, 33, told Repubblica TV.
Capello, who is now a firefighter, said he immediately called his fellow firefighters for help, as well as his family members to let them know he was OK.
"Its one of the most busy roads and it is unthinkable that something like that could happen in Italy," he said.
It was unclear from the interview with Repubblica TV exactly how Capello got out unharmed.
The Morandi Bridge, which connects highway traffic between Italy and France, collapsed on the eve of Ferragosto, a major summer holiday in Italy when Roman Catholics celebrate the Assumption of Mary. At least 39 people, including three children, were killed and another 15 were injured, authorities said.
Investigators are trying to determine the cause of the incident.
The Italian cabinet on Wednesday declared a 12-month state of emergency for Genoa, with Prime Minister Giuseppe Conte calling the bridge's collapse "unacceptable in modern society."
Meanwhile, hundreds of rescue workers remain at the scene in a desperate search for more survivors. Buildings beneath the bridge were damaged in the collapse and authorities are concerned that what's left of the structure could crumble.
"It continues to be a rescue operation until they have searched all the rubble," Italian fire official Emanuelle Gissi told ABC News on Wednesday. "They finished one side of the river bank and moved to the other side."
ABC News' Clark Bentson, Ben Gittleson and Lena Masri contributed to this report.