Sinn Féin's justice spokesman Gerry Kelly said the policing issue can be resolved after Northern Secretary Peter Hain appealed to the party to engage with the PSNI and the British government on the issue.
Mr Kelly was responding to a speech on Sunday night by Mr Hain at the MacGill Summer School in Glenties, Co Donegal, where he exhorted Sinn Féin to start preparing the way for the party to endorse the PSNI.
Mr Kelly said the "vast majority of nationalists and republicans believe that the issue of policing remains an unresolved matter which can be sorted out", and that Sinn Féin had clearly set out the issues to be resolved.
"The core issue is the transfer of powers away from securocrats in London and the Northern Ireland Office and into the hands of democratically-elected politicians in Ireland," said Mr Kelly.
Enabling legislation that would allow the transfer of responsibility for policing and criminal justice to a restored Northern Executive when there is political agreement is currently proceeding through Westminster.
The DUP has indicated that even were devolution reinstated it would not then sign up to transferring these powers to the Northern Executive.
Mr Kelly said what was needed was the enactment of this legislation and a timetable for the transfer of these powers.
"These are essentially political issues which could be resolved by political parties and the governments quickly if the political will existed.
"The obstacle to this is the DUP refusal to discuss this issue or to be involved in the institutions of the Good Friday agreement."
SDLP Assembly member Dolores Kelly said Mr Hain appeared to be allowing Sinn Féin to "cherry-pick" on policing, and that he should "not be providing more wriggle room" for the party on the issue.
Ms Kelly added: "Sinn Féin has got to sign up for a lawful society at street level as well as in the accountable policing institutions, including the Police Ombudsman's office.
"Peter Hain did enough damage tinkering with the Parades Commission to suit the Orange Order and the DUP. He should think long and hard before he tinkers with the policing arrangements to suit Sinn Féin and the Provisional movement."
Ulster Unionist Party policing spokesman Fred Cobain said Mr Hain's speech indicated that the British government was being "insufficiently robust with republicans" and ensured that they "don't have to stretch themselves too hard over policing".
"The choreography and scene- setting continues, but once again Peter Hain's strategy is flawed - too little pressure is being exerted on republicans."