Repubblika activists have filed a judicial protest against the Prime Minister and Home Affairs minister, calling on them to order an investigation into the case of Iosif Galea.
The investigation, the activists believe, would serve to establish all the facts and provide the public with all the information about the case.
Galea, a former gaming authority official, is under arrest in Italy as part of an investigation into tax evasion by German authorities.
Addressing a press conference outside the law courts on Thursday, Repubblika president Robert Aquilina said although the government had ordered its own internal inquiry, this was "not enough".
Aquilina said that the decision to have an internal investigation as a opposed to an inquiry as laid out in the law, had several limitations.
Home affairs minister Byron Camilleri said on Monday the police have launched an internal investigation into its failure to arrest Galea.
"The internal investigation would not have access to all the information related to the case. It also does not guarantee accountability and transparency," Aquilina said.
Aquilina said the public deserves to know that the police force is not led by "the attitude of impunity" that had been rife in recent years and while former commissioner Laurence Cutajar was at the helm.
The NGO is arguing that while the board is tasked with "investigating and reporting anything to do with the force" the law prohibits it from obtaining all the documents and no police officer can be made to provide such information.
According to Repubblika, the board can never go through a document that can "harm Malta's international relations". The board will also not be allowed to look into any document that might potentially prejudice an ongoing investigation.
"With these limitations, it will be impossible for the board to establish the facts and to come up with recommendations, including those for criminal action," the NGO said.
The board, the NGO said, should be given the power to examine all the documents and correspondence as well as any electronic communication on all the European arrest warrants issued against Galea.
Aquilina also highlighted the fact that Galea was arrested while holidaying with former prime minister Joseph Muscat.
"The fact he was arrested while with Joseph and Michelle Muscat is a source of suspicion and worry. Naturally, the fact Galea was in the company of the former, dishonoured prime minister raises doubts that until the arrest by the Italian police, he was being protected by Muscat or people close to him," Aquilina said.
Lawyer Jason Azzopardi signed the protest.