Mark Butler says the Albanese government is considering a tougher crackdown on visa overstayers but conceded Labor would not pursue a Trump-style enforcement model.

The Health Minister said visa overstayers are already subject to detention and deportation, but said the government is developing a broader plan to bring migration down further.

“We’ve got a single target. We’re going to have a single carefully developed plan. Unlike what you saw over the course of the last few days from the Opposition. But there are already resources going into visa overstays,” Mr Butler told Sunrise on Friday morning.

He rejected comparisons with the US Immigration and Customers Enforcement agency (ICE), saying the government would not be looking to enforce a similar model in Australia.

“They’re not, you know, of the type you just showed in the United States. And I can’t see our country going down that pathway,” he added.

Mr Butler said visa overstaying was a “significant issue” in Australia’s net migration figures, while arguing temporary migration remained important to industries including international education and healthcare.

“You know, temporary migration is a good thing for our country. State of Victoria, for example, the biggest export earner is international education,” he said.

“I can tell you, as the Minister for Health and Aged Care and Disabilities, those services rely very heavily on migrant workers. It’s a good thing, but we expect people to do the right thing and their visa. Visa overstay is a significant issue.”

The Coalition has backed tougher enforcement, with Deputy Opposition leader Jane Hume claiming the number of unlawful non-citizens has risen to more than 77,000.

“Let’s face it, the government has missed its own migration targets every single year that it has been in power — every single year. And there are rules already in place. It’s just that the government has chosen not to enforce them properly,” Ms Hume said.

She said a Coalition government would target chronic over stayers as well as people engaging in what she called “visa hopping” — moving between different visa categories to extend their stay.

“This form of visa hopping is essentially allowing people to abuse our system. Sometimes they do it using our legal aid to pay for it. That’s unacceptable,” she said.

“We want to make sure that if you are a non-citizen, an unlawful, an unlawful, lawful resident in Australia, that you go home. There are systems in place already. You just got to enforce them well.”