Rescuers dicing with choppy seas are searching for 200 asylum seekers after their overcrowded wooden ship sank off Indonesia's main island of Java. So far only 33 people have been found alive.

Two were children, aged eight and 10, found clinging to the debris of the boat five hours after the accident.

"It's really a miracle they made it," said Kelik Enggar Purwanto, a member of the search and rescue team.

The boat – packed with 250 people fleeing economic and political hardship in Afghanistan, Iraq, Iran and Turkey – was heading to Australia when it ran into a powerful storm 20 miles (32km) off Java's southern coast late on Saturday.

It was hugely overloaded, carrying more than twice its capacity, said Lieutenant Alwi Mudzakir, a maritime police officer overseeing rescue operations.

As strong waves rocked the vessel, panicked passengers started shoving one another, causing it to sway even more violently, he said.

Authorities were losing hope of finding any more survivors on Sunday.

With thousands of miles of poorly policed coastline, Indonesia is a key transit point for smuggling migrants. Many risk a dangerous journey on rickety boats in the hope of getting to Australia, where they face spending years in crowded, prison-like detention facilities. Australia's harsh immigration policy has loosened up in recent months, however.

Those on the ship had passed through Indonesia's capital, Jakarta, days earlier without any legal immigration documents, according to police.

An unidentified group loaded them on to four buses and brought them to a port, promising to get them to Australia's tiny Christmas Island.

Local television showed half a dozen survivors at a shelter in Trenggalek, the Javanese town closest to the scene of the sinking, some with dazed, empty expressions as they sat on the floor drinking and eating.

Several others were taken to hospital in critical condition.

One of the survivors, 24-year-old Afghan migrant Esmat Adine, told the official Indonesian news agency, Antara, that when the ship started to rock, people were so tightly packed they had nowhere to go.

"That made the boat even more unstable," he said, adding that he and others survived by clinging to debris until they were picked up by fishermen.

He said at least 50 of the asylum seekers were children.