Crown prosecutor Mark Dean said one of the men underwent weapons and explosives training at Al-Qaeda's Al Farooq camp in Afghanistan and was committed to jihad, or holy war.
He told the Victorian County Court that the men, all from the southern city of Melbourne, were helping a group of terror suspects in Sydney purchase laboratory equipment to make explosives.
Outlining the prosecution case, Mr Dean said a witness who attended the Al Farooq camp had heard Shane Kent, 29, pledge in the presence of bin Laden to commit jihad.
Mr Dean described another of the 13 men, cleric Abdul Nacer Benbrika, 46, of the Melbourne suburb of Dallas, as the spiritual leader of the group.
He recounted a conversation in which the cleric allegedly pledged to die for the cause.
"If we want to die for jihad we have to do maximum damage, maximum damage, damage to their buildings and everything and damage their lives. Just to show them that's what we have been waiting for. You have to be careful. Trust no one," Dean quoted the cleric as saying.
High security surrounded today's court proceedings.
Only seven of the 13 men were in court, with the other six remaining in custody at Barwon Prison.
Ten of the men were among 18 Muslims detained in Sydney and Melbourne last November, while the other three were arrested in March.
They face a range of charges including membership of a terrorist organisation, and financing and supporting a terrorist organisation.
The committal hearing before magistrate Paul Smith continues.