Extending the powers of a new UK crime fighting agency to Northern Ireland would revive decades-old concerns about police unaccountability and corruption, nationalists claimed.
Sinn Fein and the SDLP vetoed the establishment of the National Crime Agency (NCA) in the region because it would only be answerable to Home Secretary Theresa May. They faced unionist and Home Office warnings that they were opening the door to criminals.
The organisation would help target gangsters involved in drug smuggling, fuel fraud or cyber-crime.
Senior Sinn Fein Stormont assembly member Gerry Kelly said: "We are not going to go back to those days where there was a lack of accountability and with all that caused.
"We are still dealing with the legacy of that."
He added: "The experience in the past is that it will lead to corruption."
The Home Office has warned that the people of Northern Ireland could face a greater threat from crime gangs because Stormont politicians have refused to grant the new agency full powers.
Most policing and justice powers have been devolved from Westminster to the Northern Ireland Assembly, including strict scrutiny arrangements for law enforcement agencies.
Mr Kelly, who scrutinises the Police Service of Northern Ireland (PSNI) on the Policing Board, told the Northern Ireland Assembly many of the claims about the NCA refusing to give information on issues like child exploitation until its remit was not extended to the region were myths.
But Stormont Justice Minister David Ford said: "We are effectively asking some law enforcement agencies to operate with one arm tied behind their backs."
Democratic Unionist Board member Jonathan Craig said: "As the only part of the UK with a land border with another country (the Republic) we are inviting the criminal fraternity into Northern Ireland."
The NCA will target crime gangs across the UK and internationally. It is taking over from the Serious Organised Crime Agency.
The NCA chief Keith Bristow will be directly accountable to the Home Secretary, not to the PSNI, the Policing Board or the Police Ombudsman who investigates police actions.