Britain's most senior soldier feared a global escalation of the crisis and refused General Clark's requests to send an air assault team into Pristina airport to block Russian forces.
"I'm not going to start the Third World War for you," General Jackson apparently told the American commander.
In the hours that followed General Clark's order both men sought political backing for their stance but only General Jackson received it, according to the magazine Newsweek.
News of the rift comes just days after US officials announced that General Clark, who oversaw the air campaign, would be stepping down early from his Nato post.
Trouble flared between the two men as soon as the air strikes were ended and General Jackson was appointed commander on the ground in Kosovo, says Newsweek. Talks on Russia's role had broken down and the American general was so anxious to stop the cold war enemies from stealing a march on the allies he ordered British and French troops to take the airport. But the order was rejected by General Jackson.
The American then asked his fellow American Admiral James Ellis, in charge of Nato's Southern Command, to land helicopters on the runways to prevent giant Russian Ilyushin transport coming in. However, Admiral Ellis also refused, saying General Jackson would not like it. The transport planes were prevented from landing after US officials persuaded Hungary to deny them permission to overfly the country.
When the American travelled to Kosovo on 24 June he complained to General Jackson that his orders were not being followed and was answered with the comment about Third World War.