Most of the Sept. 11, 2001, hijackers were Saudis, but the kingdom has long denied any involvement in the attacks. Pictured: An American flag is pictured at the Sept. 11 memorial in New York City. Massimo Pizzotti/Getty Images

The U.S. Senate passed a bill Tuesday that would allow the families of victims of the Sept. 11, 2001, terror attacks to sue the Saudi Arabian government, multiple outlets reported. The move comes despite serious reservations from the White House concerning the bill.

The legislation, called the Justice Against Sponsors of Terrorism Act, passed in the upper chamber by a unanimous voice vote. Sen. Chuck Schumer, D-N.Y., said the bill was the result of bipartisan work with Sen. John Cornyn, R-Texas, according to the Hill.

"This bill is very near and dear to my heart as a New Yorker because it would allow the victims of 9/11 to pursue some small measure of justice," Schumer said. "[This is] another example of the Cornyn-Schumer collaboration, which works pretty well around here."

Most of the Sept. 11 hijackers were Saudis, but the kingdom has long denied any involvement in the attacks that killed about 3,000 people. But a recent report in the Guardian, citing a Republican member of the 9/11 commission, suggested that Saudi officials could have been involved in the support network for the terrorists.

The bill still has to get through the House of Representatives and be signed into law by President Barack Obama. If that happens, Reuters reported, the legislation would allow lawsuits to move forward in federal court as lawyers attempt to connect the Saudis to the attacks on the World Trade Center towers and the Pentagon.

The bill has been divisive on both sides of the aisle, finding supporters and detractors in each party. House Speaker Paul Ryan, R-Wis., previously expressed reservations.

"I think we need to review it to make sure that we're not making mistakes with our allies and that we're not catching people in this who shouldn't be caught up in this," he said to reporters in April.

The White House previously threatened to veto the bill over fears of retaliatory lawsuits aimed at U.S. citizens abroad, reported CNN.