Amsa said it had been coordinating efforts with Indonesia's search and rescue authority Basarnas. It earlier said the vessel was thought to be about 116km southwest of West Java.
The location is within Indonesia's maritime search and rescue zone.
"We have received information about a boat in distress from Australia, but we are not in touch with the boat and have no other information about it,'' Basarnas spokesman Gagah Prakoso said before the boat was found.
"We are getting ready to send a C-130 Hercules plane to drop off things like life jackets to the stricken boat. We also have 150 personnel getting ready for rescue efforts.''
Amsa said after receiving the distress call it had issued a broadcast to ships in the area, advised the stricken vessel to head for the nearest land and requested assistance from Australian border protection ships and aircraft.
Australian Home Affairs Minister Jason Clare earlier said the vessel was motoring its way back to Indonesia but authorities were taking the distress call seriously.
"The boat has rung, said it's in distress, that it's taking on water,'' he told the Australian Broadcasting Corporation. "Whenever you have a call like that, you take it seriously.
"If the vessel is sinking, if the vessel cannot make it back to Indonesia, we will have HMAS Wollongong on the scene, as well as any merchant vessels that might be available, to rescue the people on the boat.''
More than 5,200 asylum-seekers have come to Australia so far this year on boats, many of which are fragile, wooden vessels from transit hubs in Indonesia.
-AFP