The transfer of the powers is expected to top the agenda when First Minister Peter Robinson and Deputy First Minister Martin McGuinness meet Prime Minister Gordon Brown in London on Wednesday.
But after the DUP suffered a dramatic drop in support in the European election there has been speculation it may opt to delay the devolution process to appease hardliners, despite Sinn Fein demands for progress.
Sinn Fein and DUP divisions on the issue disrupted the work of the power-sharing administration at Stormont last year, before a deal was agreed on the way forward.
And while no date for devolution was declared, there was speculation it could be completed by Autumn of this year.
Mr McGuinness said: "The elections are over and the dust has settled. People have had time to digest the results."
"Over 85% of those who turned out voted for parties which support the power sharing and all-Ireland institutions."
"It is now time to move decisively ahead, get on with the job we are elected to do."
"There are a number of outstanding issues which need to be satisfactorily resolved including the transfer of powers on policing and justice."
Sinn Fein topped the poll in the election with 26% of the vote.
The three European Parliament seats available in Northern Ireland were won by Sinn Fein, the Ulster Conservatives and Unionists, with the DUP taking the third seat.
The DUP vote plummeted from 32% in 2004 to 18.2%, while the hardline Traditional Unionist Voice seized nearly a 14% share of the vote after campaigning against sharing power with republicans.
Speculation
The strong showing for TUV leader Jim Allister has fuelled speculation that the DUP leadership might come under pressure from within its own ranks to delay the devolution of the policing powers.
But Mr McGuinness said: "This issue was not a contentious part of the recent election campaign."
"These matters should not be allowed to become subject to electoral concerns by any party or government."
"They are commitments which must be implemented.
"These matters will form the basis of our discussions with the British Prime Minister tomorrow."
The Assembly and Executive Review Committee was in London for talks with Justice Secretary Jack Straw as part of its work on the mechanics of the devolution process.
The DUP has flagged-up concerns over whether government will provide the necessary funding.
Secretary of State Shaun Woodward has said, however, that government will not allow finances to jeopardise the move.
Timing
The devolution of the powers was promised in the St Andrews Agreement that paved the way for establishing the power-sharing government led by the DUP and Sinn Fein.
But last year the two parties clashed over the timing of the devolution process.
Sinn Fein accused the DUP of dragging its feet on the issue after the unionist party said the necessary community confidence did not exist for the move.
Executive meetings were stalled for five months as a result of the dispute before the parties agreed a new way forward.
The blueprint set out a process leading to the transfer of the powers, but it did not specify a date for when the move would be completed.
The devolution process will see the creation of a Justice Minister at Stormont.
It is predicted that the Alliance Party will hold the post after the DUP and Sinn Fein agreed that neither of them would take the job at this stage.
'Not ready'
The UUP has, meanwhile, expressed concerns that the Stormont regime is not ready to take on the policing powers, which it said may prove too divisive.
DUP Assembly member Jimmy Spratt was among the delegation from the Assembly and Executive Review Committee meeting the Justice Secretary.
The committee will also speak to officials in Edinburgh and Dublin to review how justice powers are administered elsewhere.
Mr Spratt said: "It is a unionist ideal for policing and justice powers to be returned to Stormont."
"Our forefathers fought for the powers to be devolved to Stormont and we protested when they were taken away."
However, these powers can only be devolved in the right circumstances.
"There are many issues, not least the financial impact of devolving these powers, which must be resolved prior to transfer."
"One issue for the meetings in London and Scotland is that of legal aid."
"The legal aid bill in Northern Ireland is three times higher than other regions of the United Kingdom."
"The work already carried out by the committee has highlighted a range of previously uncosted areas."
He said that after finance is secured, other institutional arrangements must also be in place for the powers to be devolved.
He added: "The DUP is determined to make progress on all of these issues, but we will continue to ensure that Northern Ireland is not rushed into devolving powers which will actually cost the community to administer through a reduction in other services."