Australia's Tamil community say the 157 boat people taken to WA's remote Curtin detention centre after more than six weeks at sea must be allowed to apply for protection visas.
Bala Vigneswaran, from the Australian Tamil Congress, said the circumstances of the asylum seekers' interception by a Customs and Border Protection boat on June 29 made their case unique.
"They were stopped outside Australian waters and on the request of the minister were taken into the Australian territory, so they can't be called illegal maritime arrivals," Dr Vigneswaran said.
"They were brought to Australia on the basis of an Australian Government decision and what the migration lawyers believe is that the illegal maritime arrivals regulations may not apply."
The group, 150 of whom claim to be Sri Lankan Tamils and at least 37 are children, left the Indian city of Pondicherry on or about June 12, headed for Christmas Island.
When their boat's engine started leaking oil, they called Australian authorities for help on June 26 and were intercepted three days later, about 27km north-west of Christmas Island.
They were detained on the Customs boat Ocean Protector until yesterday when they were transferred to Cocos Island before being flown to Curtin detention centre on three planes, including one chartered from Nauru Air.
Some of the asylum seekers appeared visibly relieved to have ended their 6 1/2-week odyssey, even if their future remained uncertain. Some could be seen smiling while being shuttled ashore on a Customs Zodiac.
The Indian High Commission will be allowed to offer consular access to the asylum seekers inside Curtin - a potentially controversial move if the people are seeking asylum from India.
Refugee lawyer David Manne said that because the asylum seekers had been brought onshore, they were entitled to the ordinary protection of the Australian legal system.
"Under Australian law, these people could and should be given the opportunity to make claims for refugee protection in Australia under a fair and proper process and be granted protection if found to be refugees," Mr Manne said.
Greens senator Sarah Hanson-Young said she would go to the detention centre this week to check on the children's welfare and to brief the asylum seekers on their rights. "Just because Tony Abbott wants to trade in their lives, doesn't make it legal," she said.
Mr Abbott said he expected a "very large number" of the asylum seekers would be returned to India or Sri Lanka.
The last time a boatload of asylum seekers was brought onshore was December 19.