Scott Morrison apologises for robo-debt

Prime Minister Scott Morrison has apologised for his government's controversial and unlawful robo-debt scheme.

"I would apologise for any hurt or harm in the way that the government has dealt with that issue," he told parliament on Thursday.

"Of course, I would deeply regret - deeply regret - any hardship that has been caused to people in the conduct of that activity."

The government is paying back $721 million to 373,000 people chased for debts through the unlawful program.

The scrapped scheme matched Australian Taxation Office and Centrelink data to claw back overpaid welfare payments.

It is now the subject of a class action challenge.

Mathias Cormann, the government's leader in the Senate, backed Mr Morrison's apology.

"That is appropriate for the prime minister to do," he told the upper house.

Senator Cormann said the prime minister spoke for the government, but stopped short of apologising in response to three questions from Labor's Senate leader Penny Wong.

"Of course, it should not have happened in a way that was unlawful," he said.

Labor's government services spokesman Bill Shorten said the robo-debt scheme caused psychological trauma to the thousands of people issued debt notices.

"This was a very arbitrary exercise in crude and thuggish standover fundraising by the government on the most vulnerable Australians," he told parliament.

"What we need to recognise here is this is a scandal and the greatest shame of all is we don't know how much it's going to cost taxpayers."

Government Services Minister Stuart Robert said government debt collection programs would restart eventually.

"We will do it sensibly, we will do it engaging all people and we will do it in a very transparent manner," he told parliament.

Mr Robert said about 939,000 Australians owed the government a collective debt of more than $5 billion.

Government ministers have previously refused to apologise.