The bipartisan bill has yet to make it to the Senate floor, but already it has triggered outrage in Riyadh and threatens to become a thorn in the already strained ties between Washington and its longstanding Gulf ally.
The Justice Against Sponsors of Terrorism Act would allow the families of 9/11 attack victims to sue the Saudi government for damages.
No official Saudi complicity in the Al-Qaeda attacks has been proven, and the White House opposes the draft law.
The New York Times reported Saturday that Saudi Foreign Minister Adel al-Jubeir told lawmakers in Washington last month the kingdom would be forced to sell up to $750 billion in treasury securities and other assets in the United States to avoid having them frozen by US courts.
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Secretary of State John Kerry reportedly said in February that the congressional bill could "expose the United States of America to lawsuits and take away our sovereign immunity and create a terrible precedent."
Former senator Bob Graham, who co-chaired the 9/11 congressional inquiry, told CNN Saturday that he is "outraged but not surprised" by the Saudi warning on assets.
"The Saudis have known what they did in 9/11, and they knew that we knew what they did, at least at the highest levels of the US government," Graham told the network's Michael Smerconish.
In February Zacarias Moussaoui, dubbed the 20th hijacker, told US lawyers that members of the Saudi royal family donated millions of dollars to Al-Qaeda in the 1990s.