"We must not allow sanctuary for terrorism - not for terrorists or for their money," Mr Clinton said in his weekly radio address. "It takes money - lots of it - to build the terrorist network bin Laden has. We'll do our best to see that he has less of it."
America has banned transactions between the US and companies or individuals linked to Mr bin Laden. The move is part of a systematic campaign which, it is increasingly clear, has been under way for at least a year against the former Saudi businessman. But until now it has remained largely covert, both because of security issues and because the US wanted to avoid embarrassing or angering Saudi Arabia - Mr bin Laden's family owns a large construction empire in the Kingdom.
Two attempts were made earlier this year to arrest Mr bin Laden in Afghanistan; both are thought to have failed because of the lack of co-operation from Mr bin Laden's Afghan hosts, the Taliban.
The US has also accumulated a large dossier of accusations directed at Mr bin Laden, the contents of which were shown to US Congressmen after the missile attacks on Sudan and Afghanistan on Thursday. The presentations were convincing enough to make those who had previously criticised the President for using the strikes to divert attention from his domestic problems. Senator Dan Coats, a Republican critic of the President, had said immediately after the strikes that he wanted to know more about the timing, and was harshly critical. After the briefing, he said, somewhat sheepishly: "There does appear to be credible evidence to suggest that targeting an Osama bin Laden terrorist training site was necessary."
The evidence laid out to Congress consists of satellite photographs of the camps in Afghanistan, telephone intercepts and indications that bomb attacks were aimed at embassies in Albania, Eritrea, Malaysia, Pakistan, Uganda, Egypt, and Yemen. America seems to have been expecting some sort of action in east Africa, and CIA employees were said to have been investigating Mr bin Laden's connections in east Africa before the bombings.
But the evidence consists mainly of claims about previous attacks on US or other targets, most of which were detailed by the President and other officials publicly last week. Some were not: notably, attacks on two US facilities in Saudi Arabia in 1995 and 1996. The investigations into the 1996 Khobar Towers bomb has degenerated into name-calling between US and Saudi officials, since Saudi Arabia has refused to countenance the possibility that it had a domestic source. Mr bin Laden wants the US out of Saudi Arabia, and has also sought to intervene in the extremely delicate question of the Saudi royal succession.
The US has pressured Saudi Arabia discreetly to clamp down on Mr bin Laden and had already intended to ask Crown Prince Abdullah to prevent him from drawing on assets in Saudi Arabia when the Prince visits the US later this year. Saudi Arabia, for its part, had sought to broker a deal with the Taliban just last month that would put a stop to Mr bin Laden's activities, although he would be allowed to remain in Afghanistan. That has clearly fallen through.
America says that because of cloud cover over Afghanistan, it is still difficult to assess the damage done by Thursday's attacks. But it seemed to be moving towards a less ambitious view of what had been achieved, saying that while some sites had been destroyed, others were only moderately damaged and some were untouched. US officials have suggested that more strikes may be necessary.
There is still considerable doubt over the attack on the buildings in the suburbs of Khartoum, which the US said was a chemical weapons plant and Sudan insists was a pharmaceutical factory.
A British engineer who helped construct the factory said yesterday that it could not have been used to manufacture chemical weapons. Tom Carnaffin of Hexham, Northumberland, worked for four years as a technical manager for the Baaboud family, who own the pharmaceutical plant.
"I have intimate knowledge of that factory, and it just does not lend itself to the manufacture of chemical weapons," he claimed.
Focus, pages 22, 23