"I can assure people that I weighed public safety very heavily in the decision I made.
"I can understand why people want an explanation, but for legal reasons and to maintain the integrity of that process, I cannot and will not divulge the information I used to make that decision."
National Party leader Simon Bridges said that he would have deported Sroubek.
"No ifs, no buts, a National Government would not have let in a kick-boxing, fraudster, gang-associate drug dealer like this. We just wouldn't."
He questioned the credibility of the information the decision was based on.
"They've been sold down the river with a tale that immigration officials and courts get every day of the week. They're being naive."
Sroubek came to New Zealand from the Czech Republic in 2003 after fleeing corrupt police who wanted him to lie and clear the main suspect in a murder investigation.
He fled with a doctored passport but was unmasked in 2009 when Czech police gave New Zealand police details of his identity and an arrest warrant on minor charges in connection with the 2003 murder.
Sroubek was discharged without conviction after being found guilty of using a false passport in 2011. Judge Roy Wade said Sroubek would be in danger from corrupt Czech authorities if he were deported.
Bridges said the Government needed to explain its decision, "maybe not to the nth detail, but in general terms they should be able to tell us what's going on".
"I reckon the reason they won't is that they can't. They know it doesn't stack up."
National's justice spokesman Mark Mitchell said he was prepared to travel to the Czech Republic to find answers.
"Some of the information I have would show that the threat to him is probably his own mates, because he's been involved in organised crime in the Czech Republic. Actually, that doesn't qualify you for New Zealand residency."
Ardern said the information in front of Lees-Galloway was more than simply Sroubek's own claims.
"There is other information provided. Of course, you can't simply make decisions based on someone's word."
Sroubek already had residence but it had been in the name of Jan Antolik, the name he used on his false travel document.
Lees-Galloway's move gave him residence in his real name, conditional on him not being convicted of any offence, not using any fraudulent identity, and not providing false information to a Government agency for the next five years.
In 2016, Sroubek was jailed for five years and nine months after being convicted of importing 5kg of MDMA with a street value of $375,000.
He was previously acquitted of committing an aggravated robbery with two members of the Hells Angels.
Lees-Galloway said Sroubek had yet to provide a valid travel document in his true name, which he needed to for the visa.
"The pathway forward lies with him. He's got to make some decisions about how he plans to live his life, whether he can provide the information and meet the requirements that have been put in place."