The Northern Secretary, Mr Murphy, has said a deal to restore the Stormont institutions can be agreed by the political parties.
He was speaking yesterday before a round of bilateral meetings with the parties, though not including the Ulster Unionists, under the auspices of the Belfast Agreement review at Stormont.
A paper has been drawn up outlining the progress made in the review to date. That review continues today with an Irish Government delegation present for talks on issues relating to the North-South and East-West dimensions of the agreement.
The British and Irish governments meet again in London on Friday for a half-day of intensive contacts designed to lay the groundwork for informal contacts over the summer with a view to a more concerted push for an accord in September.
Sinn Féin is to press the two premiers on Friday for intensive efforts to find a deal, while the DUP wants to put re-routed Orange parades at the top of its agenda.
Despite this, a well-placed source told The Irish Times last night that "basic agreement" had been arrived at by the parties concerning the outstanding issues.
Each party had its particular emphasis on various issues, ranging from paramilitary activity to unionist willingness to work the Stormont institutions and North-South bodies.
British sources admit the pace of attempts to find agreement has slowed, but are adamant that it has never been abandoned. Mr Murphy said the current stalemate served no purpose.
Sinn Féin fears that unionists and the governments are dragging their heels. The party released a statement yesterday reiterating Mr Gerry Adams's claim during his Bodenstown address on Sunday.
Mr Conor Murphy said: "the governments are allowing unionism and, in particular, a party which has clearly declared itself against the Good Friday agreement and which refuses to accept and respect the mandates of others, to set the pace in the process. This is unacceptable."
The party feels that the DUP is playing a "long game" and waiting for further electoral gains in next year's elections.
This has been fuelled by a statement released last week by the DUP deputy leader, Mr Peter Robinson. In it he said his party was upgrading its election targets to include all those currently held by unionists.
Mr Robinson said it was more important to have a stable agreement rather than an early one. This would take time to secure, he warned.