Dr Jarrod Gilbert, a trustee of the group and sociologist at the University of Canterbury, has appeared before Parliament's law and order select committee, and argued the case for a Government-funded commission.
He said previous research had estimated there were at least 20 people in prison, after being wrongly convicted of serious crimes.
Dr Gilbert, who is also a Herald columnist, was joined by Dr Anna Sandiford, who runs a forensic science consultancy and often appears as an expert witness in court.
Dr Sandiford said the threshold for getting a case before the Court of Appeal was high - requiring new evidence or lawyer misconduct during trial, for example.
"My experience of these cases is that things have gone wrong before they have got to trial. It tends to be involved in relation to the investigation process, the science can be poorly done or not done adequately."
Dr Gilbert said the NZPIP was "run on the smell of an oily rag", largely relying on volunteers, including University of Canterbury law students.
He acknowledged that many prisoners wrongly claimed innocence - "everyone in prison is innocent" - and said the project had been inundated since it began operations a couple of months ago.
However, if the Government were to establish a commission it would not "open a great floodgate".
"If we look at the UK, 30 per cent of cases brought before that committee are thrown out immediately because they don't meet the criteria, and only 6 per cent will go forward or be referred to the Court of Appeal.
"We are talking about a fairly modest number. But of those, 64 per cent are upheld, so they are righting injustices."
Labour MP Phil Goff told the submitters that as Justice Minister in 2004 he had asked officials to look at the issue, with a view to establish a commission.
"It felt quite wrong for me, albeit spending hours looking at these royal prerogative cases, as a member of the executive to make a decision as a lay person to overturn a decision of the judiciary."
The Royal prerogative of mercy is a constitutional safeguard that provides an avenue for convicted persons to seek a remedy in cases where a miscarriage of justice may have occurred.
The Governor-General acts on the advice of the Minister of Justice, who seeks advice from the Ministry of Justice, which can seek assistance from Queen's Counsel or retired judges.
Justice Minister Amy Adams said she was satisfied the current system was capable of correcting miscarriages of justice, through appeals or the royal prerogative of mercy process.
A body like a Criminal Cases Review Commission performed exactly the same function as the royal prerogative of mercy, Ms Adams said.
