If the intelligence study is true, it makes it unlikely that Mr Clinton will persuade North Korea, with whom the US is negotiating, to allow full inspection of its nuclear facilities. But Pentagon officials warn that he has no clear military option because it does not know where North Korea conceals its plutonium or nuclear devices.
In North Korea, the Foreign Minister, Kim Yong Nam, has rejected mediation by the United Nations because the US and North Korea are already engaged in talks. Earlier, the UN Secretary-General, Boutros Boutros-Ghali, who is on a three-day visit to the North Korean capital Pyongyang, offered to mediate over North Korea's suspected development of nuclear weapons.
The CIA's assessment, revealed yesterday by the New York Times, is based primarily on the excessive amounts of plutonium which North Korea has produced at its Yongbyon nuclear power reactor. But it is unclear if US intelligence has fresh information about progress made by the North Koreans in making a trigger to detonate a bomb.
The growing crisis over North Korea's nuclear programme was touched off earlier this year when UN inspectors were refused access to nuclear sites. They particularly want to see two waste dumps to find out how much plutonium the North Koreans already possess.
There has been a continuing dispute in Washington over North Korean aims and progress in developing a nuclear industry. The State Department's research and intelligence organisation believes there are divisions among the country's rulers. The CIA believes they want to cling to power by developing a bomb.
An alternative analysis is that the North Koreans see the threat to making their own nuclear bomb as the one bargaining chip which would enable them to escape the economic and political isolation in which they have lived since the Korean war.
If the North Koreans do abandon their nuclear programme, they will want full US diplomatic recognition, an end to the economic embargo and the possibility of foreign investment. This explains why they have rejected UN mediation in return for talks with the US. The South Korean press said last week that progress was being made in these negotiations.
President Clinton has publicly said North Korea will not be allowed to develop a bomb, but there is a limit to what he can do about it. Economic sanctions would be effective only if supported by China which said at the weekend that it was not interested in doing so. Pentagon officials have spoken of the danger of provoking a North Korean attack on South Korea.
A surprising aspect of the intelligence agency study is that, although it concludes that North Korea probably has a nuclear bomb, the evidence is largely circumstantial. Its existence is not confirmed by any satellite picture, agent's report or electronic intercept.
Senior Japanese intelligence officers believe that North Korea probably cannot obtain nuclear triggers for a bomb even if they have siphoned off some 12lb (5.4kg) of plutonium. US officials say they detected craters near Yongbyon which might be a sign that the North Koreans are experimenting with conventional explosives which are used to detonate a nuclear device.
The CIA, accused of under- estimating Iraq's nuclear programme in the late-1980s, may now be eager to protect itself by emphasising the possibility that North Korea has a bomb. But the publicity given to its assessment will embarrass the White House, which has limited means with which to exert pressure on North Korean.