Scott Morrison has shot down an overture by Labor aimed at breaking the political deadlock over Nauru, declaring “you don’t horse-trade on border protection”.

Labor on Tuesday proposed three amendments to government legislation designed to close off re-entry to Australia for any asylum seekers resettled in New Zealand – legislation the opposition has previously rejected outright, and the shift was welcomed by several Senate crossbenchers.

Labor says it's prepared to agree to NZ travel ban to get children off Nauru Read more

Other high-profile figures, including the former human rights commissioner Gillian Triggs, have backed the bill as a pragmatic solution to get children and families off Nauru, and lower house crossbenchers have urged the Coalition and Labor to come to an agreement.

Morrison put New Zealand resettlement back on the table last week on the condition parliament supported the Coalition’s lifetime ban bill, but on Tuesday the prime minister rebuffed Labor’s repositioning, suggesting the proposed amendments could have perverse consequences.

The home affairs minister, Peter Dutton, escalated the public pushback in question time, saying there were 13 children on Nauru involved in family groups “that are the subject – adults, mostly males, within that family unit – are the subject of adverse security assessments from the United States”.

Dutton queried whether New Zealand would take people for resettlement when the US had advised Australia “that person, that individual, in the family unit is a risk to national security”.

“Is the Labor party suggesting that Australia should take those males and bring them to our country? Is that what they’re suggesting?” Dutton said. “Are they suggesting that we should separate the children from the parents, leave the parents in Nauru but bring the children here?”

Both Morrison and Dutton said on Tuesday the government was dealing with what the Australian Medical Association has characterised as an “humanitarian emergency requiring urgent intervention”.

A Senate estimates committee heard evidence that 11 children were removed from Nauru on Monday. Guardian Australia understands removals from Nauru have gathered pace amid growing calls for all refugee children and families to be removed from the island, and because of a growing public backlash that found a focal point in the Wentworth byelection.

Morrison told reporters “to the best of my knowledge” Labor did not seek advice from border protection agencies before suggesting amendments to the lifetime ban bill, and he said the government would be guided by that advice.

Officials from the Department of Home Affairs conceded there was no need for the government to pass its lifetime visa ban legislation in order to accept New Zealand’s longstanding refugee resettlement offer.

On Monday night the departmental secretary, Mike Pezzullo, confirmed there were already ways to flag individual former asylum seekers to stop them returning, and that the new laws were wanted to allow for “blanket directions”.

He said while watchlists existed, they needed “an apparatus to get that certainty in law”.

“Any non-Australian citizen is able to be placed on a movement alert list,” Pezzullo told the estimates hearing.

Asked to explain, Pezzullo said he didn’t want to “go too deeply into operation tradecraft”, but essentially the person’s intention to travel would be flagged with the department at check-in.

“Why would I bother considering passing [the lifetime visa ban bill] if you can’t tell me that it would secure an outcome?” asked the Labor senator Louise Pratt.

She said Labor was being pressured to pass the legislation, and presented as the ones blocking the resettlement of sick children.

Pezzullo said “unless that backdoor is closed” it does make resettlement prospects more difficult, “unless the parliament deals with the legislation currently before the Senate”.

New Zealand is the only country whose citizens can obtain a visa on arrival in Australia. There is growing controversy about the number of Kiwis being deported under section 501 of the Migration Act, relating to character grounds and criminality, even if they have lived in Australia since infancy.

Those individuals could already be flagged for re-entry refusal, as can refugees resettled in the US under the deal with the former Obama administration, estimates learned.

Under further questions, Pezzullo and other department officials also confirmed that those who had been resettled in the US could apply for a visa to visit Australia, but indicated it was likely they could be refused entry on the grounds of having “illegally” breached Australia’s borders with their original asylum attempt.

Pezzullo also confirmed that at least “as a matter of law” New Zealand was under no strict obligation to ask permission from Australia to take the refugees. He said previous statements from successive New Zealand prime ministers suggested they hoped to find a collaborative and cooperative arrangement.

The Greens senator Nick McKim told Guardian Australia: “The travel ban legislation has always been a political position of the LNP rather than a practical necessity.

“It reinforces our opinion that all of the children and families on Nauru should immediately be brought to Australia for medical assessment and treatment.”

He said the Greens would not support the bill in its current form.