The BBC says that America's special agents backed away from the bin Laden family soon after George W Bush became president.
Agents were also told to back off the Saudi royals - although that has all changed since September 11.
The findings come from documents obtained from the FBI investigation of the US terror attacks by the Newsnight programme.
The papers show that despite the myth that Osama is the black sheep of the family, at least two other American-based members of it are suspected of links with a possible terrorist organisation.
Newsnight says it has uncovered a long history of shadowy connections between the State Department, the CIA and the Saudis.
The former head of the American visa bureau in Jeddah from 1987 to 1989, Michael Springman, told the programme: "In Saudi Arabia I was repeatedly ordered by high-level State Department officials to issue visas to unqualified applicants.
"People who had no ties either to Saudi Arabia or to their own country. I complained there. I complained here in Washington to Main State, to the Inspector General and to Diplomatic Security and I was ignored."
He added: "What I was doing was giving visas to terrorists - recruited by the CIA and Osama bin Laden to come back to the United States for training to be used in the war in Afghanistan against the then Soviets."
The US allegedly wanted to keep the pro-American Saudi royal family in control of the world's biggest oil spigot, even at the price of turning a blind eye to any terrorist connection - so long as America was safe.
The programme said the younger George Bush made his first million with an oil company partly funded by the chief US representative of Salem bin Laden, Osama's brother, who took over as head of the family after his father Mohammed's death in a plane crash in 1968.
Story filed: 03:10 Wednesday 7th November 2001
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