The hour-long meeting, reviving the Hume-Adams dialogue that paved the way for the ceasefire 17 months ago, came at a time when Mr Adams is increasingly isolated.
Since the London Docklands bomb, both the British and Irish governments have said their ministers will not meet him, and it was reported yesterday that the US government was considering denying him an American visa. Sources in Washington said a final decision had not been taken.
Mr Hume said after seeing Mr Adams: "We discussed the restoration of the peace process. It was an in-depth discussion. I believe that if a common-sense approach is now taken, we can restore that process."
Mr Hume said he would meet John Major in London tomorrow. "I will be discussing the overall situation with the Prime Minister, including my suggestions for breaking the log-jam to restore the peace process."
Mr Hume is arguing for a referendum, north and south of the border, to record a "people's verdict" against violence and in favour of an early start to all-party talks to determine the future of Northern Ireland.
Peace hopes were also bolstered last night by a cautious agreement on the part of the Ulster Unionists to talk to the Dublin government. David Trimble, the new Unionist party leader, wrote to Dick Spring, the Irish deputy prime minister, proposing talks - but with conditions. He warned that it was not simply a problem of dates: "We need to agree on an agenda."
On the Peace Convention favoured by the British government and the Unionists, he said this body would be elected within Northern Ireland and would primarily operate there. "It would not therefore be appropriate for the Irish government to be involved in discussions relating to the creation or operation of that body. Still less would it be right for the Peace Convention to be jointly sponsored by the Irish government."
As for Mr Adams, his current US visa lapsed about 10 days ago, according to a British embassy official in Washington. "The impression is that the visa will not be renewed automatically; they are keeping their options open."
A spokeswoman at the State Department said: "Our first task is to get the ceasefire restored and our decision on Mr Adams's visa will be made in due course."
Mr Trimble, who saw the US President last week, disclosed yesterday that during their conversation Mr Clinton said it was "damn stupid for them to resume violence when they did".
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