"Despite the claims of fear of being sent back to the Czech Republic, he was voluntarily going back there and living in plain sight," National's immigration spokesman Michael Woodhouse said.
"One way or another, this fellow is not worthy of staying in New Zealand and he should be sent home."
But Lees-Galloway says he has no intention of resigning, and expected Immigration NZ to report back to him within three weeks.
He said it was "not standard practice" to see all the court documents relating to Sroubek before making his decision.
"It is the practice I inherited from the previous Government ... It would be a worthwhile exercise to reflect on that and see if there are improvements that could be made."
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 on.
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.
National's justice spokesman Mark Mitchell said he had been in touch with retired immigration officers and police detectives who had dealt with Sroubek.
"Just about every single Kiwi this guy was put in front, [they] completely rejected [his story] and saw it for what it was.
"The only one who seems to have really drunk the kool-aid on this is the minister and the prime minister."
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 for 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 previously acquitted of committing aggravated robbery with members of the Hells Angels, but in 2016, was jailed for five years and nine months for importing 5kg of MDMA.
Police Minister Stuart Nash said he was surpised when he learned about the case.
"It was quite a shock to read, but I was assured by the minister there are mitigating factors," he told Newstalk ZB.
Lees-Galloway said he could understand public indignation about a convicted criminal being granted residency while serving time.
"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 dealt with the case because Sroubek was eligible for parole.
The Parole Board declined parole in September, 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.
Q&A
Who?Karel Sroubek, from the Czech Republic, arrived in NZ in 2003 on a false passport under the name of his friend Jan Antolik.
What about him?Immigration Minister Iain Lees-Galloway granted him NZ residency despite Sroubek's gang associations and convictions for using a false passport and drug-smuggling, for which he is currently in prison.
Sroubek was originally granted NZ residency under the name Jan Antolik, but Lees-Galloway granted him conditional residency under his real name.
Why was he given residency?Lees-Galloway has not revealed the reasons, citing legal reasons, but has now ordered an investigation into claims that could negate the information he initially relied on.
What claims?He will not discuss the claims, but a High Court judgment revealed that Sroubek travelled to Europe in 2009, which would challenge any notion that his life might be in danger if he were deported.
What now?Immigration NZ will investigate the claims and report back to the minister within three weeks.