The National Party says the identities of immigration officials who processed residence applications from service head Mary-Anne Thompson's relatives should be revealed.
The applications were approved despite being filed late and at a time when the quota for people living in Kiribati was full.
Ms Thompson helped themembers of her extended family fill in the forms, and signed her name as having done so.
An independent report, released last week, cleared Ms Thompson of having tried to influence the processing of the applications but it said staff were instructed to override policy.
All the names and positions of the staff involved were deleted in the version of the report released to the media - including those who issued the instructions.
National's immigration spokesman, Lockwood Smith, said today he did not see why the deletions were necessary.
"Why should officials, doing official work, have their names deleted?" he said on Radio New Zealand.
"The privacy strikes me as being rather odd. Where officials are carrying out their official functions, they should be accountable for their actions."
Dr Smith said he was not going to let the matter rest, and he is expected to ask questions in Parliament when the recess ends early next month.
The report was prepared by former justice secretary David Oughton at the request of the Labour Department, which is responsible for the Immigration Service.
"There are serious issues raised in it," Dr Smith said.
"It makes clear that the abuse of protocols was not uncommon, so we've obviously got quite a widespread problem.
"We think we've got certain immigration rules that let certain people in but what this report indicates is that people get in if the boss wants them to come in."
Dr Smith likened it to the Ingram report into allegations against former Labour MP Taito Phillip Field.
The Government accepted the report's findings but Dr Smith's persistent questioning of ministers in Parliament raised a number of new issues.
Mr Field, now an independent MP, is facing 15 charges of bribery and corruption alleging he accepted work on seven of his properties by Thai nationals in return for immigration assistance.
