The wife of Czech drug-smuggler Karel Sroubek says the Deputy Prime Minister calling her a National Party informant has increased fears for her safety, National Party justice spokesman Mark Mitchell says.

National has demanded Immigration Minister Iain Lees-Galloway resign over his handling of the Sroubek case, after he was initially given New Zealand residency despite being in prison for smuggling MDMA.

Lees-Galloway, who said he is staying put to fix the system, last week issued a new deportation liability notice to Sroubek following an Immigration NZ review of the case.

Today Mitchell criticised Deputy Prime Minister Winston Peters for calling the wife a "National Party informant" while speaking on behalf of Prime Minister Jacinda Ardern during Question Time last week.

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"She's not. She is a victim who is the subject of a police safety plan," Mitchell said today.

"But the Deputy Prime Minister attacked her anyway. Now her family has even greater fears for her safety, saying Mr Peters has 'placed a fair and square target on the back ... of a vulnerable young woman already dealing with enough challenges under the circumstances'."

Peters again spoke on behalf of Ardern during Question Time today, and said that National had not denied that the wife was an informant.

"That question was put to Parliament last week, and there was no answer from the National Party then, not a mutter, not a murmur."

When told that the wife had first contacted a former Labour Party Minister for help, but was told to contact the Opposition because the Government wasn't going to change the decision, Peters said: "So she is the informant, then."

Under questioning, Lees-Galloway said the wife had declined to participate in the Immigration NZ review.

Lees-Galloway said he has treated and continues to treat the safety of all those involved in the case very seriously.

"For that reason, I will not comment further on matters concerning these people."

But Mitchell said that she had told Immigration NZ officials that "she was happy to help but would want her lawyer and support person present, and was frightened of the target on her back becoming bigger".

Mitchell also claimed that Immigration NZ arrived at her house unannounced on November 5 at an address "known only to police as part of a police safety plan".

Immigration NZ general manager Nicola Hogg said officials visited the wife with police after a "thorough risk assessment", which was standard practice.

"On this occasion, one Immigration NZ official was accompanied by two police officers during this visit. Immigration NZ stands by this approach."

She said the wife declined to participate at a subsequent meeting in which her lawyer was present.

"At this meeting, Immigration NZ also apologised for any distress caused by the initial visit and explained the reasons for the approach."

Mitchell, who said he was in touch with people close to the wife, said she was "under duress" when she supported Sroubek's case at the start of the process.

"She doesn't want him to stay and has changed both her phone number and address, because of what she says are threats to her safety.

"The family of Mr Sroubek's ex-wife have rightly had enough. They say Mr Peters has caused immense stress 'and a feeling of utter hopelessness'."