But this morning, a spokesman for the Prime Minister said she still has confidence in Lees-Galloway.
"As she has consistently said, she has confidence in the minister, not the decision," the spokesman said.
Lees-Galloway maintains that he was thorough in making his decision, and has since gone back, read the entire case file, and stands by the decision based on the information he had at the time.
On Thursday, under questioning from National, Lees-Galloway conceded that he made the decision about Sroubek, who is in prison for drug-smuggling, on the same day he received the case file.
He later admitted he did not read the whole file, and made his decision "within about an hour or so".
"I read various aspects of the full file. I didn't rely solely on the summary. This is the usual process for these decisions.
"I took much, much longer on this decision than I have on other decisions, and I'm following exactly the process that I inherited from the previous minister."
Immigration NZ general manager Stephen Dunstan said the process for absolute discretion by a minister has been in place since 2003, and it was not unusual for decisions to be made on the same day that the files arrive.
He said a case file could be up to 100 pages long, depending on how complex it was.
"The time-frame is really up to the minister. Some decisions are made on the same day. Sometimes ministers might ask questions or request further information," Dunstan said.
Ardern and Lees-Galloway have said they are open to reviewing the process, following the investigation into Sroubek's case.
National has continued to press Lees-Galloway in the House, and he has repeatedly declined to answer questions about the Immigration NZ review, saying he does not want to prejudice the review or any legal action that might follow.
On Thursday, National's deputy leader Paula Bennett used parliamentary privilege to reveal an allegation that Sroubek threatened his estranged wife in a phone call from prison in May this year.
On Wednesday, she used Question Time to expose an alleged burglary of a $2.3m house just days after Sroubek placed a caveat on it, and on Tuesday she referred to court documents to reveal that a family was placed in a witness protection programme because of Sroubek's alleged actions.
Sroubek released a statement through his lawyer, saying he had nothing to do with the alleged burglary and was acquitted in the trial that involved the witness protection programme.
"Comments made about that case in the media are not balanced, and in particular do not reflect that the key prosecution witness' evidence was discredited," Sroubek said.
"Much of what has been said about me and my circumstances does not present the true picture.
"Until Immigration NZ reports backs to the Minister and I have had the opportunity to respond to him on any issue he may wish to raise, I will be making no further comment or statement."
