Asylum seekers on a boat intercepted by ACV Triton at the weekend were reportedly screened by Australian officials with a four-question procedure via video link, according to Fairfax Media.
Lawyer Julian Burnside says if the reports are correct then Australia could be guilty of breaching international law.
The government has repeatedly refused to confirm reports that two boats have been intercepted by Australian authorities off Christmas Island in the past week.
One of the boats is reportedly carrying 153 Tamil asylum seekers, including about 30 children - many of them sick - while the other has 50 people aboard.
Mr Abbott said the government has always acted within the scope of international law, refusing to confirm media reports on the screening process of asylum seekers.
"There does need to be a process because we do have international obligations," he told 3AW radio.
"But I want to make this observation: Sri Lanka is not everyone's idea of the ideal society. But, but it is at peace - a horrific civil war has ended and I believe there has been a lot of progress when it comes to human rights and the rule of law in Sri Lanka."
There have been conflicting reports on the Sri Lankan navy's response.
One navy official told the Australian newspaper that some asylum seekers would be transferred to Sri Lankan custody. But another official has denied that a Sri Lankan navy vessel has been dispatched to facilitate a transfer, the Guardian reported.
Mr Abbott also defended the government's decision to reserve the right to turn back asylum seeker boats.
"We said before the election that one of the policy options that we reserve the right to use when it is safe to do so is turning boats around. And it's no secret that some boats have been turned around. So look without making any particular comment, I just want to assure listeners that what we're doing is consistent with our international obligations and consistent with safety at sea."
Opposition immigration minister Richard Marles said the reports are disturbing, accusing the government of treating Australians with contempt by refusing to confirm or correct the claims.
"The whole question about operational matters being used as a veil to prevent legitimate questions about the public interest has always been a farce," he told ABC radio.
"If those reports [on asylum seeker screening processes] are correct, this would appear to be a fig leaf in order to throw out the human rights handbook. And the only reason for doing that is to protect a political scoreboard. That would be very concerning."