Prime Minister Tony Abbott says the government would never stop people to randomly check their visas.
Mr Abbott says his office had no prior knowledge of the Australian Border Force operation in Melbourne and the agency simply issued a poorly worded press release.
"Obviously it was a mistake," he told reporters in Sydney on Saturday.
"We will never be in the business of stopping people randomly in the street to check on their visa details."
A public backlash forced the cancellation of the Border Force crackdown on Friday.
Operation Fortitude was intended to be a joint operation between Victorian Police and the Australian Border Force.
Prime Minister Tony Abbott said the incident had been explained and that there was no need for any agency to take responsibility.
"Nothing untoward happened except for the issue of a poorly-worded press release. I know there are people in our community who don't like the Government's strong border protection policy. I know there are people out there in the community that don't like this Government," he said.
"I want to make it absolutely crystal clear, as far as this Government is concerned, people will never be stopped in the street randomly and asked for theireesa details. That's the sort of thing that would never, ever happen in this country."
Mr Abbott also defended the work of the Australian Border Force.
"I think people are really pleased that under Australian Border Force there has been a 75 per cent increase in air cargo screening, there has been a 25 per cent increase in sea cargo screening," he said.
"The idea that they should be pilloried on the basis of a badly-worded press release just shows that some people readily get things completely out of proportion."
Former independent MP Tony Windsor, who is considering a return to politics, said the cancelled visa spot check operation was part of the federal government's national security agenda.
"I've got no doubt that some of these people in Abbott's government hope that something goes wrong domestically - that they can taunt a Muslim into doing something," he told ABC radio on Saturday.
Victoria Police called the operation off after a "high level of community interest" and Police Minister Wade Noonan said the government had originally been told it would target anti-social behaviour and aim to get commuters home safely.
Victoria's Police Minister is blaming the cancellation of Operation Fortitude, which was to include random visa checks in Melbourne this weekend, on the Australian Border Force.
Wade Noonan said he was told it was to be a standard police operation until the ABF's announcement that it would be speaking to any individuals it crossed paths with in the Melbourne CBD.
After online outrage about the random spot checks, the ABF clarified they wouldn't be stopping people at random.
The federal opposition has demanded the Immigration Minister provide an explanation.
"What we have witnessed in the last six hours has been a complete debacle on Peter Dutton’s watch," he said.
“Mr Dutton needs to immediately explain to the community what on earth has transpired.
“Who sanctioned this announcement being made, what was its purpose, who called for its retraction and who is responsible for compromising this operation?”
Greens senator Sarah Hanson Young said the explanation of a "clumsily worded" press release is inadequate.
"It wasn't just a clumsily worded statement. This is a clumsily run department, headed by a klutz of a minister. This was a part of a militarisation, a toughening up of Australian Border Force," she told the ABC.
- with AAP
