The container ship, the Fesko Askold, has 17 crew on board.
It arrived in Pago Pago on Sunday afternoon and sailed out of the main harbour at nine yesterday morning.
It remains about eight kilometres from shore.
American Samoa's COVID-19 task force chairman Iulogologo Joseph Pereira said this would allow local authorities to complete their assessment of the situation and come up with a plan to offload and pick up containers.
He said steps had been taken to decontaminate the dock in case of any contamination while the vessel was dockside.
Pago Pago port was scheduled to reopen this morning after a 24 hour shutdown.
Iulogologo Joseph Pereira said while two separate tests had been conducted, affirming the positive results for the three crew members, a third battery of tests was being done by the more sensitive and sophisticated ABI7500 Testing Machine at LBJ Medical Center.
The government was not aware of protocols being adopted by the vessel's captain to contain further spread of the virus to other crew members, he said.