The Taoiseach and British Prime Minister have begun round-table table discussions in St Andrew's in Scotland with Northern Ireland's political parties.
Arriving for the negotiations, DUP leader Ian Paisley said that for Sinn Féin to give their support to policing should mean providing information to help solve terrorist crime and also handing back their 'ill-gotten gains'.
The Irish and British governments are describing the meeting as a unique opportunity to break the political deadlock ahead of the 24 November deadline.
Speaking on RTÉ Radio's Today with Pat Kenny, the Northern Secretary, Peter Hain, said he believed a deal was possible.
However, Mr Hain also stressed that London was serious about closing down the Stormont assembly if the politicians did not meet the deadline.
At a rally in Belfast last night, the Sinn Féin President, Gerry Adams, insisted his party was opposed to criminality of all kinds and wanted policing that was fair and impartial.
Last night's speech by Mr Adams is being seen as having acknowledged that if a party wants to be part of a power-sharing government it must actively support the institutions of law and order.
It is also being seen as the strongest signal yet that Sinn Féin may be willing to address the greatest concern of unionists.
The next three days are set to tease out what moves Ian Paisley's DUP is prepared to make.
Cautious optimism - Background to the Scotland talks
Three developments in the past week have led to a positive yet cautiously optimistic atmosphere ahead of today's talks.
A positive assessment of IRA inactivity from the Independent Monitoring Commission, the meeting between Ian Paisley and Archbishop Sean Brady and a call for movement towards acceptance of policing structures by Gerry Adams last night are not only symbolically significant but have given genuine grounds for optimism.
Both the governments and the parties accept that key issues remain, principally policing and the stability of the institutions, but neither seem insurmountable.
Both the Taoiseach and the British Prime Minister know a lasting resolution would dwarf their domestic difficulties and in Mr Blair's case would represent a substantial element of his legacy.
A peace deal will neither be agreed nor triumphed come Friday but the governments hope that real progress can be made particularly on the question of policing and this will form the catalyst for a renewed push for a deal prior to 24 November.
The parties are expected to hold a round table meeting upon arrival to set out their negotiating positions and concerns.
A dinner is planned for both Wednesday and Thursday night before the two Premiers hold a concluding press conference around lunchtime on Friday prior to the departure of the respective parties.
The British government must convince Sinn Féin that there will be minimal delay in the transfer of justice and policing powers to any new Stormont administration.
Sinn Féin must convince the DUP that they are committed to backing the policing structures and upholding law and order.
The DUP must convince republicans that they are ready, willing and able to administer a power-sharing administration which has republicans at its heart.
Dr Paisley will be central in guiding his party to accept any deal which may be hammered out over the coming weeks.
Many within his party may seek to have any such deal endorsed by the wider unionist population in the form of an election but others within the DUP will want to give any administration time to bed down before any election would take place.
