The National Party is rejecting claims it could have deported the Czech drug smuggler Karel Sroubek while it was in power.
Tuariki Delamere, who was the minister in the late 1990s, helped Sroubek gain residency in 2008.
He said former National ministers Jonathan Coleman, Nathan Guy and Michael Woodhouse all failed to deport him when they could.
But Mr Woodhouse told Checkpoint it never came across his or any other National Minister's desk because Sroubek had been arrested on other crimes and couldn't be deported.
Sroubek is at the centre of a firestorm in New Zealand after Immigration Minister Iain Lees-Galloway confirmed his residency and stopped him from being deported. The case is now being reviewed by Immigration New Zealand.
"Lees-Galloway was the first minister to see the file," Mr Woodhouse told Checkpoint.
Immigration New Zealand has confirmed Lees-Galloway was the first and only minister it alerted about the case.
It said it only puts deportation cases to the minister once they have a full account of the case and provided Mr Lees-Galloway with all the relevant information they had at the time.
Mr Woodhouse also said he has more information about Sroubek that he would reveal it shortly.
He said it only took a few days to gather significant information about Sroubek and that Mr Lees-Galloway had more than enough to deport him.
"He should have made a better decision," he said.
Mr Woodhouse said he has information that Sroubek did return to the Czech Republic but has been unable to verify it.
Mr Lees-Galloway has refused to say why he decided to allow Sroubek to remain in New Zealand, citing privacy and legal reasons.
"[Sroubek's] appeal was a Hail Mary request that was agreed to by a naive and gulliable minister," Mr Woodhouse said.
"This doesn't even come close to the suspension of a deportation order."
Mr Woodhouse said he and fellow National MP Mark Mitchell have been overwhelmed by the number of people who have come forward to share information about the nature of Sroubek.
Sroubek has reportedly claimed that he fled his home country because he feared for his safety.
Prime Minister Jacinda Ardern said the handling of the case was not good enough.
She said the immigration minister made a decision on the information he had at the time, but three weeks was too long for an investigation and she wanted answers as quickly as possible.
Mr Lees-Galloway launched an investigation into the case on Thursday, saying he'd become aware of new allegations that could contradict the information he relied on to make his decision.
Earlier in the day, RNZ revealed the existence of a 2009 court judgment which showed Sroubek, under the name Jan Antolik, was given permission to travel to the Czech Republic while on bail and that he'd already been back to Europe earlier that year.