Bruce Morrison, a former US congressman, who acted as a conduit between Sinn Fein and the US government said: "What they wanted from the States was clarity that Sinn Fein would once again achieve access to the States and access to the White House and ability to do fundraising - things that they had achieved in the first ceasefire."
Mr Morrison told BBC Radio 4's Today programme that Sinn Fein had wanted assurances that there would be "some sort of attention to deportation cases that were of concern", and "perhaps overriding of all, continued engagement of the President towards a negotiation process."
When asked if President Clinton had been personally involved, he said: "These items which they raised with me were raised with the White House, with the National Security Council, and then ultimately through them with the President. And he signed off on a response which conveyed back and gave necessary assurances in the areas I have mentioned."
He added that the discussions with republicans had been in terms of an unequivocal cessation of violence. Mr Morrison will meet with Ms Mowlam later this week, following her meeting with Mr Adams, the Sinn Fein leader, today - the first such meeting since before the previous ceasefire.
Meanwhile, there were indications that tensions over the planned Apprentice Boys' parades in Northern Ireland were easing last night as both sides adopted an increasingly non-confrontational stance to the Royal Ulster Constabulary's decision to re-route the parades.
Police confirmed that they had served notice on the Apprentice Boys that they must re-route parades in two nationalist villages and in Belfast's Lower Ormeau Road.
A spokesman for the Bogside Residents, Donncha MacNiallais, said yesterday evening that the Apprentice Boys' march through Londonderry on Saturday should be allowed to go ahead without interference.
The group has called off a number of "counter marches" that had been planned for Friday night. Mr MacNiallais asked that the Union flag should not be flown on Saturday from a planned position overlooking the Bogside. But he said he was "quietly confident" that events would pass peacefully on Saturday, when up to 12,000 Apprentice Boys are expected to march.
Apprentice Boys groups are expected to meet later this week further to discuss the RUC's decision. But while governor Alistair Simpson said they were disappointed at the re-routing, he said he had received assurances that they would act within the law.
Apprentice Boys' spokesmen stressed that although they were not entirely happy with yesterday's conclusions, the main concern was that the weekend should pass off peacefully.
Mr Simpson paid tribute to the SDLP mayor of Derry, Martin Bradley, for attending a loyalist function the previous evening. He is believed to be the first nationalist mayor to attend a function at Apprentice Boys' headquarters.Reuse content