Immigration NZ is investigating claims that contradict the reasons why Iain Lees-Galloway granted residency to convicted drug smuggler Karel Sroubek.

Immigration Minister Lees-Galloway made the announcement this afternoon but is remaining tight-lipped about which claims are being look at, declining to comment on reports that Sroubek's wife no longer supports him and is seeking a restraining order against him.

It has also emerged that Sroubek traveled to Europe in 2009 and returned to New Zealand, in accordance with strict conditions of his bail at the time.

Radio NZ reported that the information is from a 2009 decision in the Auckland High Court. Lees-Galloway said he had not seen the court judgement.

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National Party leader Simon Bridges has said that if Sroubek had traveled to the Czech Republic, it would challenge any notion that his life might be at risk if he were deported.

Lees-Galloway said the claims were serious and asked Immigration NZ to report back within three weeks, but he was not going to make any decisions based on hearsay or innuendo.

If the contradictory information stacks up, it could mean that Sroubek may have committed an offence under the Immigration Act - which could trigger liability for deportation or criminal charges.

Lees-Galloway also revealed that he granted residency to Sroubek even though it wasn't asked for, saying it was the only way to achieve the outcome that he had decided was the right one.

Sroubek had previously been granted residency under the false name Jan Antolik.

"In order to suspend deportation, a new visa needed to be issued in the correct name," Lees-Galloway said.

The minister has been under pressure since it emerged that he granted residency to Sroubek, even though Sroubek was found guilty of using a fake passport and is currently in jail for smuggling MDMA.

Sroubek came to New Zealand on a false passport from the Czech Republic in 2003, but was unmasked in 2009 when New Zealand police were given details of his identity and an international arrest warrant on minor charges.

In 2011 he was found guilty of using a false passport, but was discharged without conviction on grounds that he would be in danger from corrupt Czech authorities if he were deported.

He was acquitted of committing an aggravated robbery with two members of the Hells Angels, but in 2016, he was jailed for five years and nine months for importing 5kg of MDMA.

Lees-Galloway has not provided a reason for granting Sroubek residency, citing legal reasons and the need to maintain the integrity of the process.

National's immigration spokesman Michael Woodhouse said the investigation was being used to justify a u-turn.

"It's been handled in a ham-fisted way. He should have had this information well before he decided to make this decision, and he made the wrong decision.

"This man has been unlawfully in New Zealand for up to 14 years. [The minister] had every opportunity to send him home. He chose not to take it."

National has called for Lees-Galloway to resign, but the minister said he had no intention of doing so.

He said he could understand public indignation about a convicted criminal being granted residency.

"But these matters are dealt with on a case-by-case basis, and I have to deal with the information I have available to me at the time," Lees-Galloway said.

Simon Laurent, a lawyer who has acted for Sroubek, said it would be "quite problematic" if it was proven that Sroubek had returned to the Czech Republic.

"If he had been back to the Czech Republic, and that could be established beyond a doubt – then it would undermine the case for the minister [to grant residency]."

Lees-Galloway said the case came before him because Sroubek was eligible for parole.

The Parole Board declined parole last month, and Sroubek is due back before the board before the end of September 2019.

In rejecting parole, the board said he was a low risk of reoffending, but noted his links with criminal elements in the Czech Republic, with Hells Angels' members and called his answers "self-exculpatory, evasive, long-winded and ultimately in our view in many respects manifestly untruthful".

His sentence end date is January 2022.