The Australian Maritime Safety Authority's (AMSA) records show it alerted Indonesian authorities to a struggling asylum seeker boat, despite allegedly accusing those on board of lying about needing to be rescued.

AMSA's records show it relied on a report from a nearby oil tanker in its assessment that the asylum seeker boat was not in in trouble.

But those on board say they were frantically pumping water off the boat and feared they would sink.

Footage from the boat shows them waving life jackets at the oil tanker, in an attempt to get help.

An Afghan Hazara asylum seeker, Naqsh Murtaza, says AMSA staff refused to believe the boat was taking on water and the engine was crippled.

He says for hours AMSA told him that he was lying about the boat being in trouble and to just "fix the motor".

AMSA has not denied the allegations, but the authority's notes show that staff alerted the Indonesian rescue agency, BASARNAS, to the boat's location.

AMSA also says it alerted commercial shipping channels within about one hour of receiving the distress call from the boat and maintained contact with the asylum seekers until Indonesian authorities arrived on the scene.

The oil tanker, called the Baltic Galaxy (Panama), responded to the alert and stayed near the boat, providing reports to AMSA until the people were rescued.

BASARNAS rescued all 81 people from the boat and confirmed it was leaking and broken down.

Those on board the vessel were safely returned to Indonesia.