The initiative is being pushed forward by four prominent Irish-Americans, including Bruce Morrison, a former congressman who is a political ally and one-time law school friend of President Bill Clinton. They are due to visit Belfast for talks with Mr Adams and others late this week.
The group has been engaged for several months in behind-the-scenes efforts to persuade the IRA to end its campaign of violence, and the White House is believed to have been kept closely informed of progress.
When the group's members visited Northern Ireland last September, the IRA announced a seven-day ceasefire. They have since paid a number of visits, but when they return this week members are optimistic that a more lasting ceasefire, perhaps permanent, will begin.
'We hope we will be successful,' Mr Morrison said in an interview yesterday. 'We've continued to try to help Sinn Fein to persuade the IRA that the time has come to move from violent acts to the political arena and end the armed struggle.'
It was members of the same group, aided by the influential Senator Teddy Kennedy, who persuaded the Clinton administration to grant Mr Adams a visa earlier this year. Although there was subsequent concern that this may have been an error, the group has retained the confidence of the White House and has received support from the Dublin government.
In the past year, members of the group have held talks with Albert Reynolds, the Irish Prime Minister, and with Sir Christopher Mayhew, the Secretary of State for Northern Ireland. They have also had some contacts in the Unionist community, including the Ulster Unionist leader, James Molyneux.
Speaking late last week, members of the delegation said that in the event of a complete cessation of hostilities they expected US government aid and private investment in the Northern Ireland economy to increase dramatically.
The initiative grows out of a dramatic change in the climate of opinion among Irish-Americans prompted by the dialogue between John Hume, the SDLP leader, and Mr Adams. Once bitterly divided between opponents and supporters of the IRA, Irish-Americans have united behind the drive to support and develop the Hume- Adams process and they form a strong lobby with influence reaching to the highest levels in Washington.
Besides Mr Morrison, the members of the group are Niall O'Dowd, publisher of the Irish Voice newspaper in New York, and two leading businessmen, William Flynn, of Mutual of America, and Charles Feeney, head of the multinational General Atlantic.
In the event of an IRA ceasefire, the group believes it can persuade the US authorities to issue Mr Adams with a visa to tour the United States. It also sees Mr Clinton playing a role in pushing forward the process of finding a constitutional settlement in the province.
The initiative, and particularly the US visa for Mr Adams, are unlikely to be welcomed by Unionists. The British government, too, would have reservations about any American action that would seem to improve the standing of Sinn Fein or the IRA.
The Irish-American group expresses support for the Downing Street Declaration, which remains the key Anglo- Irish document on Northern Ireland, but the direct dealings with Mr Adams in particular threaten to shift the axis of peace-making in the province. When Mr Adams was last issued with a US visa, Britain protested strongly.
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