The delegation from the Rev Ian Paisley’s DUP was led by deputy leader Peter Robinson, along with MPs Nigel Dodds and Jeffrey Donaldson.
After the talks at Hillsborough Castle, Mr Murphy said there was a “definite seriousness” among all parties to see an end to direct rule.
He said all politicians were anxious to see theAssembly restored.
“That can only happen if they resolve the underlying difficulties that divide them,” he said.
“I do believe Sinn Féin is serious about wanting to have a resolution of these difficulties.”
The talks took place following a reminder from Mr Murphy to parties ahead of next month’s crucial peace progress negotiations in Leeds Castle in Maidstone that they were entering one of the most critical phases of the negotiations.
With the DUP and Sinn Féin needing to bridge the gap between them over the future activities of the IRA, weapons decommissioning, the stability of power-sharing institutions and the transfer of policing and justice powers, Mr Murphy said he was encouraged by some of the public comments made by unionists and nationalists in recent weeks.
“I have been pleased with what we have heard and seen,” said Mr Murphy.
“Some of the statements have been very encouraging. While there has been some difficulty over marches it has certainly not been as bad as the past.
“All of these auger well for the seriousness with which local politicians will tackle the restoration of the institution.
“The fact is we all know the issues which have to be addressed. We are at a crucial phase in the process which, as the Prime Minister said at Lancaster House, will be a point of decision.”
Several DUP figures, including Mr Robinson and Mr Donaldson, have told republicans this summer that the winding down of the IRA and conclusive disarmament would provide the basis for stable power sharing in the North.
Mr Robinson has also indicated that his party wants the devolution of policing and justice powers but believes it could be unsettling to introduce it within the early stages of a new power sharing executive.
In what was interpreted as another positive development Sinn Féin leader Gerry Adams said this month that republicans would have to consider removing the IRA as an excuse for unionists not to engage with his party.
But the West Belfast MP insisted that for the IRA to wind down, there must be guarantees from unionists that they would genuinely work the power sharing institutions in good faith.
He also insisted the British and Irish governments would have to deliver on commitments made in the 1998 Good Friday Agreement and in subsequent negotiations.
Unionists and republicans were both cautious yesterday about the prospects of a deal.
However, one political source said he believed there could be a breakthrough during the Leeds Castle talks on September 16-18.
Former US president Bill Clinton is expected to meet politicians in the province when he arrives in Belfast tomorrow for a book-signing event in the city centre.
Mr Clinton, who encouraged parties to overcome their difficulties in the run up to the 1998 Agreement and in its aftermath, is expected to urge them once again to go the extra mile to restore the Assembly and power sharing executive.