This article is more than
8 year oldThe House of Representatives held a voice vote on legislation that the Senate approved in May.
President Obama vowed again to reject the measure, but Republicans could overturn one of his vetoes for the first time if they secure enough votes.
Saudi Arabia, a key US ally, has denied any role in the attacks.
Democratic New York lawmaker Jerrold Nadler, the bill's sponsor in the House, said of Friday's vote: "We wanted it to come to the floor, symbolically before the 15th anniversary.
"We've been aiming toward that the entire session.''
President Obama has warned of retaliatory lawsuits against the US government if American citizens are allowed to take the Saudis to court.
But Terry Strada, national chair for 9/11 Families United For Justice Against Terrorism, disagreed that the bill could backfire as the White House has warned.
"If we're not funding terrorist organisations and killing people, then we don't have anything to worry about," she said.
Democratic presidential nominee Hillary Clinton, a former New York senator, is among backers of the bipartisan legislation.
Riyadh reportedly threatened earlier this year to pull hundreds of billions of dollars from the US economy if the Justice Against Sponsors of Terrorism Act was enacted.
The Saudi foreign minister warned the bill would strip the principle of sovereign immunity and usher in the "law of the jungle".
Separately, a bipartisan group of US senators announced on Thursday they will attempt to block the Obama administration's proposed sale of more than $1bn (£754m) in weapons to Saudi Arabia.
Riyadh has never been formally implicated in the 11 September 2001 attacks.
But two months ago Congress released 28 declassified pages from a report that reignited concerns a few of the attackers had links to Saudi government officials.
Last year, a confessed 9/11 plotter in US custody, Zacarias Moussaoui, claimed a Saudi prince had helped finance the attack.
The kingdom said it was a baseless accusation from a "deranged criminal".
Fifteen of the 19 hijackers were Saudi citizens.
Newer articles
<p>The deployment of Kim Jong-un’s troops has added fuel to the growing fire in recent weeks. Now there are claims Vladimir Putin has put them to use.</p>