Talks have been held between the Ulster Defence Association and the Ulster Volunteer Force to end the violence which has left four men dead in north Belfast in less than a fortnight.
Security experts believed the people involved in the talks included the most senior figure in the UVF as well as the group's leader in north Belfast, a representative of the UDA's so-called inner council and a senior member of its south-east Antrim brigade.
Earlier, a figure close to the negotiations, Mr Davy Mahood, from the Ulster Democratic Party, the UDA's political representative, said: "At least we expect a continuation of the cessation of violence which has been in place since Saturday which hopefully will result in a permanent end to the violence."
He was glad the UVF had accepted his party's point of view that talks were urgently needed to resolve the feud, Mr Mahood, the UDP's north Belfast chairman, added.
A senior RUC officer in north Belfast, Supt Campbell Dixon, said: "I hope that the steps taken today will bring an end to it and that it is not just a temporary measure."
A Sinn Fein north Belfast MLA, Mr Gerry Kelly, welcomed the talks as a "positive development" which should be encouraged by political leaders, particularly those from the unionist tradition.
The talks, scheduled for last week, were cancelled after the worsening violence which led to the death of two UDA members, Mr David Greer and Mr Tommy English, as well as two UVF men, Mr Bertie Rice and Mr Mark Quail.
The RUC has appealed for information about the killing of Mr Rice, a 63-year-old former UVF internee who had recently returned from South Africa to work for the Progressive Unionist Party, the UVF's political wing.