In the long-awaited telephone call yesterday afternoon, Mr Major told the President that Sinn Fein had to commit itself to "serious and constructive discussion designed to lead to concrete steps in decommissioning of arms" before ministers would meet them, a Downing Street spokesman said.
In what was described as a "businesslike and thorough" 25-minute conversation, the two leaders partly patched up the rift over Mr Clinton's welcome for the Sinn Fein president, Gerry Adams, at the White House.
Mr Clinton met some of the British government's objections on Friday when he insisted publicly that the IRA should start to get rid of its weapons.
But the Prime Minister made his irritation clear over American clearance for Mr Adams to raise money in the US.
Downing Street said that Mr Major told the President "that there was a long history of funds raised in the United States being used to support the IRA's activities and that it was vital that money should not be used to re-stock the IRA's arsenal.
"The President said that the US government wanted to see strict accounting for funds raised by Sinn Fein in the United States."
Mr Major's insistence that ministers would not yet meet Sinn Fein contrasted sharply with upbeat comments from Martin McGuinness, the Sinn Fein vice- president, who said in interviews yesterday that he expected talks with ministers to start in the next 10 to 14 days.
He said there was nothing in the agenda, discussed at meetings between Sinn Fein and civil servants, to delay talks.
Mr McGuinness suggested that Sinn Fein did not feel it had to fulfil any further preconditions. "We will not advance any further in the process unless we all agree to talk to one another, and that has to be the next stage in the process," he told GMTV's Sunday Programme.
But Mr McGuinness pointedly refused to give the commitment the Prime Minister wants, repeating only the Sinn Fein demand to "remove all the guns from our society".
The Ulster Unionist MP Ken Maginnis said: "What they are basically saying is that all arms are on a par, both the legal weapons carried by the security forces and the illegal guns used by the paramilitaries ... and it is totally unacceptable."
The Irish Prime Minister, John Bruton, called on Sinn Fein to make "a clear and definite offer" on the decommissioning of weapons, but said also that everything possible should be done to help Mr Adams "bring his movement with him on this issue".
Mr Bruton, who had talks in Washington last week with Mr Clinton, highlighted on Irish radio the need for the Republican movement to "make a clear and definite offer".
Mr Adams' American visit received surprising support from James Molyneaux, leader of the Ulster Unionist Party, fresh from seeing off a "stalking horse" challenge to his leadership on Saturday.
Speaking on Channel 4's A Week In Politics, he agreed that the visit had locked Sinn Fein more securely into the peace process and made a return to violence even more unlikely. "I do not think that was what he intended but, thankfully, because of a fair bit of pressure from various parts of the American administration itself, assisted by some of the rest of us at long range, the desired result was achieved," he said. He accepted that, to that extent, the visit had been a good thing.
Mr Maginnis said: "I do believe that the weapons issue is on the agenda, but in such a form as to make a mockery out of the political process."
Last week, Mr Major made clear that talks could begin without a single IRA weapon being handed in. But he insists that Sinn Fein must still give a commitment to talk about disarming the IRA.
Talks involving other parties cannot begin until that disarmament process is "substantially" under way, he said.