The Ulster Unionist Party leader, Mr David Trimble, is coming under increasing pressure to meet the Sinn Fein president, Mr Gerry Adams, face-to-face as the talks restart today at Stormont.
The former Bishop of Derry, Dr Edward Daly, has joined those calling for such a meeting, while the DUP leader, the Rev Ian Paisley, has said Mr Trimble was caught "in a cleft stick" on the issue and was "discredited".
Mr Trimble appeared to rule out such a meeting in the short term yesterday, when he was asked on the BBC's On The Re- cord programme if he would meet Mr Adams. He said he would first wait to see if Sinn Fein was "seriously engaged".
"We have got an agenda which was set by the document called Propositions on Heads of Agreement. Are they going to talk about that? So far they haven't," Mr Trimble said.
He also suggested that Sinn Fein was not genuine about seeking a settlement and did not accept that unionists had a right to a say in the peace process.
Dr Paisley said he believed Mr Trimble "couldn't win" on the question of a meeting with the Sinn Fein leader.
"Everybody is pressurising him to meet him. Clinton says he must meet the IRA, and the British government and Tony Blair is saying he must meet the IRA, and if he breaks and meets the IRA, he is finished, and if he doesn't, he is finished. So they have got him in a cleft stick," he said. The DUP leader described Mr Trimble as "another unionist leader discredited in an attempt to break up unionist unity".
Speaking in Derry at the weekend, Dr Daly, said he was now "embarrassed" that he had refused to meet Sinn Fein for nearly 15 years.
He said it was essential for people who considered themselves on opposite political sides to try to build on what they had in common and to try to resolve their differences through dialogue.
Today's discussions will deal with Strand One issues on the internal governance of Northern Ireland. Sinn Fein will put forward its argument against the establishment of a Northern Assembly, while the SDLP and the Ulster Unionists are expected to disagree on the powers such an assembly should have.
The Ulster Democratic Party, meanwhile, is continuing its efforts to be readmitted to the talks.
A party spokesman said last night a delegation would meet the UFF to convey British government reservations about the wording of its ceasefire announcement after it had admitted carrying out recent killings.
"The government considered that the statement as it stood was highly qualified, but we pointed out that it was not our language," the UDP spokesman said, adding that it would be for the UFF to decide what position it then takes, and how it would convey that.
He said it had been given no indication as to when it would be readmitted. The UDP also intends to publish its response to the two governments' paper on North-South institutions later this week.
Two men were treated for gunshot wounds after paramilitary-style attacks in the North on Friday night. In one incident a 19year-old was shot in both knees in the Ardoyne area of north Belfast. A 21-year-old suffered leg injuries in an attack in Newtownabbey.