Opposition:Ógra Shinn Féin, which entered the ardfheis in stark opposition to the leadership's stance on the PSNI, argued that acceptance of support for the PSNI would be "a massive mistake".
Ógra spokesman Senan Mac Aoidh said such a move would be against "the ideals and principles of Sinn Féin", and would underscore British imperialism and capitalism in Ireland.
The ardfheis should adopt a position alongside that of Ógra members, he added.
Also opposing the ardchomhairle motion, Luaghaidh Mac Giolla Brighde from south Derry said a vote to back the police in the North was tantamount to a vote to back British rule.
Speaking as the brother of a dead IRA member and one who opposed the entry of Sinn Féin TDs into Leinster House in 1986, he said only when republicans had influence in key positions within policing would he feel happy to support the PSNI.
"Unless we have people in day-to-day control - as chief constable, assistant chief constable - or have people who are sympathetic, we will not have control or influence over policing," he said.
But he warned: "Let no one use my analysis for splitting republicanism." Sinn Féin should engage in "guerrilla politics" and work to make the Border irrelevant.
Northern Ireland MEP Bairbre de Brún said that a vote for the ardchomhairle motion was not a vote for the northern state.
She called for a strategic debate and argued that any change should be real change. "Don't just change flags," she said. "We can't have a pale reflection of the two failed states" in Ireland.
Opposing the motion, David Glackin, Mullingar, said the primary purpose of any police force was to defend the State.
"I believe that the six-county statelet is illegitimate and a failed state and should not exist. Do not ask me to support and defend a force whose primary purpose is to defend a state that I want to see dismantled." He proposed an amendment to the motion that would have dropped Sinn Féin support for the PSNI and the criminal justice system.
Cork delegate Paul O'Connor said he and his fellow cumann members could not support the motion, since it asked them to support a British-controlled police and judicial system in the North.
"As long as there is British rule in Ireland that is simply unacceptable to us. We should not give in to blackmail. To pass this motion is to limit ourselves in the future.
"But whatever decision is reached today we will leave here united, strong and determined."
Opposing the motion, Ógra Shinn Féin delegate Morgan Fraser said: "It would be completely wrong and a massive mistake to support the PSNI."
Tullamore delegate Michael Scully said it would be wrong "to allow our sons and daughters to join a rebranded RUC".
Plastic bullets can still be used in the North, he said, despite all of Sinn Féin efforts to have them banned. "Who will decide if they are to be used again?"
Galway West delegate, Daniel Callinan, said every initiative taken by Sinn Féin had been "thrown back in our faces 10-tenfold" by the DUP and by the UUP before them.