Home Affairs Minister Jason Clare said aerial surveillance of a debris field of wood and life-jackets had spotted 13 bodies and a full-scale hunt was under way for survivors.
"This is a search and rescue, trying to find people alive," Clare told reporters, describing the incident as "another terrible tragedy, another terrible reminder how dangerous these journeys are".
When the drifting boat was first spotted by a border protection aircraft on Wednesday, Clare said officials "identified approximately 55 people on the deck of the vessel, mostly adult men but also a small number of women and children".
The Warramunga arrived on site to find wood and life jackets floating, with the first body sighted late on Friday and another 12 found by Sunday morning.
Rear Admiral David Johnston, head of border protection, said the "complex and time-consuming" task of recovering bodies would wait until the search for survivors was exhausted.
"We believe from (medical) advice that we are still in the window where survivability is possible," Johnston said.
He added that Indonesia's maritime authority Basarnas was "certainly aware of the incident" but was caught up with a number of other vessels closer to the Indonesian coastline.
HMAS Warramunga had also been diverted to assist another suspected people-smuggling boat off Christmas Island, which issued a distress call to Australian police overnight, Clare said.
Australia is struggling with a record influx of asylum-seekers arriving by boat from Indonesia and Sri Lanka, with numbers expected to top 25,000 in the 12 months to June 30 despite punitive policies banishing refugees to the remote Pacific.
