"When no-one took up the opportunity [to speak to Indian consular officials] then their reason for being at Curtin [detention centre] no longer existed," Minister Morrison told reporters in Sydney.
He confirmed that the 157 asylum seekers had been flown on three separate flights from Western Australia late last night to arrive on Nauru earlier today.
The 157 Tamil asylum seekers, among them 50 children, have been at the centre of a political storm after they were detained at sea on a Customs ship for three weeks before being flown to Western Australia last month.
Minister Morrison dismissed criticism of the decision to transfer the group to Nauru, saying the government has been clear about its offshore detention policy.
"At the end of the day people [that arrive by boats] don't end up in Australia. The government has a strong will on these issues and that will continue."
Asylum seeker transfer condemned as 'cowardly'
The decision was condemned by Greens senator Sarah Hanson-Young, who said his actions are a "disgrace" and "cowardly".
The senator was speaking at a rally in Adelaide, where she said asylum seeker children in particular were being used a "political pawns".
"They are being used as political pawns in a desperate game for the minister to look tough," she said.
"Well, you don't look tough mate. You look like a coward."
What we have is a shambles: Opposition
Opposition Immigration spokesman Richard Marles said the government had "lost control" of its asylum seeker policy and was making "policy on the run".
"This is a serious and complex area of policy but we have a cowboy in charge," he told reporters in Melbourne.
He criticised the late night transfer of 157 asylum seekers from WA's Curtin Detention Centre to Nauru, saying it was a "sneaky media strategy".
"The only reason that they [the asylum seekers] have been put through this wretched rollercoaster is to protect their [the government's] personal poiltical scoreboard that is today in tatters."
Lawyer in dark over asylum seeker clients' transfer
The lawyer for a a group of Tamil asylum seekers at the centre of a High Court challenge says he had no idea his clients were being transferred to Nauru in a secret overnight operation.
Lawyer George Newhouse said he thought they were still in Australia before learning of the move from media.
"I found out from News Corp just like everyone else," he told AAP.
"What happened, the veil of secrecy that this government has over operational matters?"
Immigration Minister Scott Morrison confirmed on Friday those on board the most recent asylum-seeker boat would not be resettled in Australia.
Claim asylum seekers were advised not to talk 'a lie'
Mr Morrison said the asylum seekers refused to talk to the Indian high commissioner and lawyers - or "boat chasers" as he called them - had advised the group not to accept a deal to be returned to India, News Corp reported.
Mr Newhouse said that was a lie.
"Any suggestion that we advised our client not to talk to anyone is false," he said.
"We have not had a proper opportunity to inform our clients of their rights and their options because of the secrecy surrounding them.
"And I am not calling him (Mr Morrison) names for sending children to an abusive environment in Nauru."