The State Government passed extraordinary laws early this morning to stop confidential documents from the Fitzgerald inquiry being published.
The CMC requested the laws after it admitted to mistakenly allowing access to thousands of sensitive documents about police corruption.
The new laws stop any confidential material mistakenly released by the CMC being published for 60 days.
The CMC requested the laws after it admitted to an "administrative oversight" that allowed access to thousands of confidential documents about police corruption.
The laws also require the Parliamentary Crime and Misconduct Committee (PCMC) to hold an open inquiry into the mistake, the CMC's delays in reporting it to the committee, and their destruction of related documents.
Mr Newman says the CMC chairman should consider his position.
"Given this pattern of a lack of openness, a lack of accountability, a lack of respect for the processes of Parliament, he should consider his position," he said.
"My concern is that we have a senior important public servant who doesn't seem to understand his responsibility or his accountability to the public of Queensland."
The CMC says it is not appropriate to comment while an inquiry into the error is conducted.
Civil libertarians have labelled the CMC unaccountable.
"I currently have a case where I'm something like 15 months into waiting for a report from the CMC and my client has been unable to work for the entirety of that time,' he said.
"There's been no remedy from the CMC - no remedy from the parliamentary committee."
However, Queensland independent MP Dr Alex Douglas says Mr Martin should not resign.
He says Attorney-General Jarrod Bleijie is wrong to vilify Mr Martin.
"What the Attorney-General did by jumping three steps ahead is to use kangaroo court justice," Dr Douglas said.
"In other words, you're prejudging that the person is guilty until found otherwise.
"In our justice system, you're innocent until proven guilty."