The boat was first spotted by authorities Wednesday, about 80 nautical miles west of Christmas Island, the Australian Broadcasting Corp. reported Sunday.
Of the 55 asylum seekers believed aboard the boat, most were men, officials said.
Four planes and two merchant ships have been used in the rescue effort.
Home Affairs Minister Jason Clare said about 13 bodies had not yet been recovered.
"This is another terrible tragedy. Another terrible reminder how dangerous these journeys are," Clare said. "This is a search and rescue trying to find people alive today and that's where my focus [is]."
"We want to stop people getting here on boats," he said. "At the completion of this search, this will be [the] subject of a full review, as is standard practice. The focus today is on finding people alive."
Meanwhile, another boat full of asylum seekers ran into trouble west of Cocos Island several days ago, the Australian Broadcasting Corp. said. A British merchant vessel picked up 78 refugees and brought them to Christmas Island.
Two other boats carrying almost 200 asylum seekers have been intercepted since Friday, the broadcaster said.