Malcolm Turnbull says the coalition makes no apologies for taking a tough approach to people smugglers.
Cabinet documents obtained by the ABC show former immigration minister Scott Morrison requested ASIO in 2013 to delay security checks so asylum seekers would miss a deadline to obtain permanent protection visas.
It is unclear whether ASIO complied with the written request.
But Mr Morrison said in a statement on Tuesday, "As minister for immigration and border protection, it was my policy and practice to put Australia's national security interests first".
The prime minister backed up his cabinet colleague, saying Mr Morrison had "stopped the boats".
"We make no apologies for sending the clearest message to the people smugglers and to their would-be customers: if you think you can come to Australia on a people smuggler's boat, you're wrong. You won't. You won't get here, you will not become a permanent resident," Mr Turnbull told reporters in Sydney.
"Keeping our borders secure is a critical obligation and responsibility of government."
Asked about two days of cabinet leaks from the Abbott era, Defence Industry Ministry Christopher Pyne said he didn't look in the rear vision mirror.
"Four-year-old stories are four-year-old stories," he told reporters in Canberra.
Opposition Leader Bill Shorten said he would examine the cabinet documents, but was concerned the government continued to mischaracterise Labor's position on people smuggling.
"We want to stop the people smugglers," he told the National Press Club in Canberra.
"When the government says Labor won't do that, they are giving a signal to the people smugglers to test our system - I wish for once they would think about the national interest and people's safety rather than trying to turn it into a partisan issue."
Labor senator Kimberley Kitching says the cabinet leaks appear to be aimed at making Foreign Minister Julie Bishop's leadership rivals Mr Morrison and Tony Abbott look bad.