Australia’s policy of deporting New Zealand citizens with criminal records has become “corrosive” to the relationship between the two traditional allies, Jacinda Ardern has said, in her strongest warning yet to Scott Morrison.

The Australian prime minister arrived in Auckland on Friday morning for a brief official meeting with Ardern and New Zealand officials, forgoing the traditional weekend stay prime ministers of both countries usually bestow upon each other.

Since 2014, more than 4,000 people have been stripped of their Australian visa and returned to their country of birth, regardless of how long ago they left. New Zealand-born Australians have made up the vast bulk of the deportations.

In a joint statement the two prime ministers “acknowledged the importance of the sensitive management of visa cancellation decisions, appeals and removals of New Zealand citizens who have been convicted of crimes in Australia, and committed to continue working together”.

But minutes later Ardern spoke far more plainly at the pair’s joint press conference, using strong language rarely directed at Australia.

“In my view, this issue has become corrosive in a relationship over time,” Ardern said.

“I’ve made it clear that New Zealand has no issue with Australia taking a dim view of newly arrived non-citizens committing crimes … but equally, the New Zealand people have a dim view of the deportation of people who move to Australia as children and have grown up there.”

Morrison told the media Australia had “very well-defined immigration and citizenship laws” and his government had “taken a very strong line” on it.

“Visas are not citizenship,” he said. “Visas are provided on the basis of people being compliant with those visas, and that doesn’t include committing crimes.

“And so we take a very strong view about this. It is a view that is not restricted to New Zealand, I should stress … this is not targeted at New Zealand in any way, shape or form.”

The 2014 changes to Australian law mandated the automatic cancellation of a visa for anyone sentenced to 12 months or more in jail.

Some of those deported have had extensive criminal histories in Australia, but no link to New Zealand beyond citizenship. Some have no family or other connections in New Zealand.

Last month dozens of New Zealanders held in Australian detention centres embarked on a mass hunger strike, and begged Ardern to intervene on their behalf, with some having been detained for months or even years in remote centres hundreds of kilometres from their families.

This week it was revealed that an Indigenous Australian man who was born in New Zealand when his parents were visiting, but had no ties to the country, was to be deported.

The Australian government is attempting to expand its deportation powers even further to include non-citizens, including minors, who are convicted of an offence that carries a maximum sentence of two years, no matter their own sentence.

Labor has said it will oppose the bill, as it potentially allows for a child convicted of shoplifting to be deported.

New Zealand maintains that only people with “genuine links” to the country should be deported.

Earlier on Friday a spokesperson for Ardern denied a report in the Australian newspaper that said New Zealand was unwilling to accept single, male asylum seekers from Nauru and Manus Island, and said the offer to resettle 150 asylum seekers remained active.

• This article was amended on 13 March 2019. An earlier version said that 2014 changes to Australia’s Migration Act allow automatic visa cancellation for anyone convicted of an offence that could attract more than 12 months in prison, even if that sentence was not imposed. This has now been clarified.