Thirty-nine people were believed to be on board the vessel when it began taking on water about 7am yesterday, a spokesman for Home Affairs Minister Brendan O'Connor said.
A total of 19 people, all males aged between 20 and 40, have been plucked alive from the sea so far, while a life raft has been dropped down to a group of between two and five people in the water, the spokesman said. Between 15 and 18 people are still missing.
The boat capsized late last night as two rescue ships moved in to try to save those on board. Australian Defence Force chief Angus Houston said the vessel was hundreds of kilometres north-west of Cocos Island and the closest Australian naval vessel was 28 hours' steaming time away.
The Australian Maritime Safety Authority received the boat's first distress call at 7.10am (AEDT) yesterday but the information was not clear and the boat's location was not pinpointed for another three hours, Customs and Border Protection said in a statement.
A Taiwanese fishing trawler was the first to respond and found the boat at 4.11pm.
"The fishing vessel made contact with the vessel and reported to AMSA that it was not sinking but was taking on water," the statement read.
"Australian authorities understand that the fishing vessel did not have the capacity to take the people on board."
The next boat to arrive was the LNG Pioneer, which travelled 12 hours at AMSA's request to the location, arriving about 11pm.
It was shortly after this that the stricken boat was believed to have capsized, Australian Defence Force chief Angus Houston said.
"I understand that when the first ship got there this vessel was still intact," Air Chief Marshal Houston said.
"Somehow or other during the process of the interaction between the ship and the trawler and also the stricken vessel, there's been a capsize."
Mr O'Connor's spokesman said the rescue ships worked in extremely difficult conditions.
"It's first light there now, but it was pitch black with no moon when [the rescue] was happening,” he said earlier today.
The LNG Pioneer rescued 15 people overnight and two more people today. The fishing trawler rescued two people, he said.
An RAAF P3 Orion aircraft spotted a group of between two and five people alive in the water and threw down a life raft to them, he said.
The survivors would most likely be sent to Christmas Island but no decision had yet been made. The final decision rested with the captains of the rescue ships, he said.
A further two aircraft were expected to join the search effort, including a Customs and Border Protection Command Dash 8 aircraft and a Royal Flying Doctor Service Hawker 800 XP jet.
An Australian vessel is also on its way but would take more than a day to reach the area.