A bill that would allow the families of 9/11 victims to sue the Saudi government has passed a key hurdle in the US Senate.
The Justice Against Sponsors of Terrorism Act (JASTA) now moves to the House of Representatives.
Saudi Arabia's foreign minister warned that the move could cause his government to withdraw US investments.
President Barack Obama said he will veto the bill, but a Democratic senator is "confident" he'd be overruled.
If it became law the legislation would allow victims' families to sue any member of the government of Saudi Arabia thought to have played a role in any element of the attack.
Saudi Arabia denies any involvement in the 2001 attack on the World Trade Center and the Pentagon, which killed nearly 3,000 people.
Fifteen out of the nineteen hijackers in 2001 were Saudi citizens.
In 2004 the 9/11 Commission Report found "no evidence that the Saudi government as an institution or senior Saudi officials individually funded the organisation".
A White House spokesman said President Obama had serious concerns about the bill, and it was difficult to imagine he would sign it into law.
It was sponsored by Democrat Senator Chuck Schumer of New York and Republican Senator John Cornyn of Texas and is expected to be passed by the House of Representatives as well.
The 9/11 bill puts Congress on a collision course with the Obama administration, which has lobbied intensely against it.
The White House argues the legislation would remove the sovereign immunity that prevents lawsuits against governments, and could expose Americans to a legal backlash overseas.
For Congress, however, this is about fighting terrorism and pursuing justice for victims, and there is unusual bipartisan support for the bill. Some of its most outspoken supporters are Democrats who are confident that Congress has the necessary two-thirds vote to override a presidential veto.
There is no evidence to support claims that Saudi officials provided financial support to the hijackers, although some believe a classified section of the report into the 9/11 attacks might show otherwise.
But Congress is also playing to the strong emotions triggered by this dispute - the relative of a victim recently told the New York Times it was "stunning" to think the government would back the Saudis over its citizens. One suspects many Americans might agree.
Senator Schumer said: "Today the Senate has spoken loudly and unanimously that the families of the victims of terror attacks should be able to hold the perpetrators even if it's a country a nation accountable.
"It will serve as a deterrent and warning to any other nation who assists in terror attacks against American."
He said he was confident the bill would be passed by a large margin in the Republican-controlled House of Representatives.
On Tuesday, Saudi Arabia denied it had threatened to sell its US bonds, which would pull billions of dollars from the US economy.
"We said that a law like this is going to cause investor confidence to shrink," Foreign Minister Ahmed Al-Jubeir said while attending a conference in Geneva. "Not just for Saudi Arabia, but for everybody".
Last year an inmate in US custody, Zacarias Moussaoui, claimed that a Saudi prince had helped finance the attack that flew passenger planes into the World Trade Center in New York and the Pentagon in Virginia.
A fourth plane crashed into an empty field in western Pennsylvania.
Saudi Arabia had rejected the accusation from a "deranged criminal" with no credibility.