The boatpeople - believed to be 14 Turkish Kurds accompanied by four Indonesian crew - were towed out to sea on Friday by the Australian Navy after their Indonesian fishing boat reached tropical Melville Island, 80km north of Darwin, on Tuesday.
The small Australian island lies outside Australia's official migration zone, which means that reaching its shores does not give them an automatic right to seek safe haven.
Australian Prime Minister John Howard has taken a tough stance on asylum seekers. He won a third term in office in 2001, due largely to strict, new measures against boatpeople. Australia's maritime borders were effectively sealed.
But human rights organisations have criticised his tough policy on humanitarian grounds.
The Supreme Court late on Friday rejected a claim by the Northern Territory Legal Aid Commission to bring the 14 asylum seekers back to Australia, but has not disclosed its reasoning or the location or destination of the boat, the Minasa Bone.
An Immigration Department official told the court a Navy ship was still towing the boat on the high seas, the Australian Broadcasting Corporation reported, but he was unable to disclose where the boat was or where it was heading.
He also revealed defence personnel were on the fishing boat, but denied this amounted to detention because the men were still free to go anywhere, except Australia.
Defence Minister Robert Hill said in a transcript posted on his website that the navy had towed the boat away from Melville Island but declined to give further details.
"It was disabled. It was repaired," he said. "If it needs to go anywhere under its own propulsion it can do so," he told reporters.
Australia has taken a hard line against people-smuggling since discovering that organised gangs were using neighbouring Indonesia as a stepping stone for Middle Eastern and Afghan asylum seekers trying to reach Australia.