WASHINGTON: US lawmakers are vowing to decisively override President Barack Obama's veto of a bill to allow families of September 11 victims to sue the government of Saudi Arabia.

Obama rejected the bill on Friday. He said the legislation could leave American troops and diplomats vulnerable to lawsuits in foreign courts from people seeking redress for actions taken by armed groups that are backed or trained by the United States.

The bill's proponents are disputing those concerns. They say the measure is narrowly tailored and applies only to acts of terrorism occurring on US soil.

The Republican sponsor of the bill, Senator John Cornyn of Texas, is criticising Obama for failing to listen to the families of the victims. Cornyn says he looks forward to the opportunity for Congress to override the veto.

Obama rejected the bill that would have allowed the families of 9/11 victims to sue the government of Saudi Arabia, arguing it undermined national security and setting up the possibility Congress may override his veto for the first time in his presidency.

Obama's move escalates the fight over an emotional issue that has overlapped with the campaign debate over terrorism and the Middle East.

The bill had sailed through both chambers of Congress with bipartisan support, clearing the final hurdle just days before the 15th anniversary of the 9/11 attacks that killed nearly 3,000 people in New York, Washington and Pennsylvania.

The president said the bill, which doesn't refer specifically to Saudi Arabia, could backfire by opening up the US government and its officials to lawsuits by anyone accusing the US of supporting terrorism, rightly or wrongly.

"I have deep sympathy for the families of the victims of the terrorist attacks of Sept 11, 2001," Obama wrote to the Senate in a veto message about the bill, the Justice Against Sponsors of Terrorism Act.

But, he said, "the JASTA would be detrimental to US national interests more broadly."

Congress is determined to try to overturn the veto, which requires a two-thirds vote in the House and Senate. Previous attempts to overturn Obama's vetoes have all been unsuccessful.

House Minority Leader Nancy Pelosi, D-Calif., has said an override would pass in the Republican-controlled House. Yet the Senate would be the greater challenge.

After furious lobbying to try to peel off supporters, the White House said Friday it was unclear whether enough had defected to avert an override.

With lawmakers eager to return home to campaign, a vote could come early next week.

Senate Majority Leader Mitch McConnell's office said the Senate would vote "as soon as practicable in this work period".

Sen. Chuck Schumer of New York, the Senate's No. 3 Democrat and a traditional Obama ally, came out swinging against Obama while predicting lawmakers would reverse it "swiftly and soundly".

"The families of the victims of 9/11 deserve their day in court, and justice for those families shouldn't be thrown overboard because of diplomatic concerns," Schumer said.

A coalition of 9/11 victims' families, meanwhile, said they were "outraged and dismayed".

In a response circulated by their lawyers, the families insisted the bill would deter terrorism, "no matter how much the Saudi lobbying and propaganda machine may argue otherwise".

Though the concept of sovereign immunity generally shields governments from lawsuits, the bill creates an exception that allows foreign governments to be held responsible if they support a terrorist attack that kills US citizens on American soil.

Opponents say that's a slippery slope considering that the US is frequently accused by its foes of supporting terrorism.

"Americans are in countries all over the world," House Armed Services Committee Chairman Mac Thornberry, a Republican, wrote Friday in a letter urging colleagues to support a veto.

"Many of those countries do not respect the rule of law, and we cannot expect their responses to be as measured and narrow as ours."

Fifteen of the 19 men who carried out 9/11 were Saudi nationals. Families of the victims spent years lobbying lawmakers for the right to sue the kingdom in US court for any role elements of Saudi Arabia's government may have played.

Saudi Arabia, a key US ally, strongly objected to the bill.

Obama long had objected, too, warning that foreign countries might reciprocate by dragging American government, diplomats and military members before courts.

The administration was also apprehensive about undermining a difficult yet strategic relationship with Saudi Arabia. The US relies on the Saudis to counter Iran's influence in the Middle East and help combat the spread of terrorism.

Since the bill's passage, the White House has lobbied aggressively to persuade lawmakers to withdraw support, and found some sympathetic listeners.

The bill had passed by voice vote — meaning lawmakers didn't have to go on the record with their positions and the White House was hoping the prospect of a recorded vote would lead some Democrats to reconsider publicly rebuking their president.

Debate about the bill has spilled onto the presidential campaign trail, as candidates vie to appear tough on terrorism. The issue is one of a few where Democrat Hillary Clinton, who supports the bill, has publicly disagreed with Obama.

Trump, too, backs it, and said Obama's veto was "shameful and will go down as one of the low points of his presidency".

The bill had triggered a perceived threat by Saudi Arabia to pull billions of dollars from the US economy if it was enacted. Saudi Foreign Minister Adel bin Ahmed Al-Jubeir said in May the kingdom never issued threats, but had merely warned that investor confidence in the US would shrink if the bill became law.

The House vote on Sept 9 came two months after Congress released 28 declassified pages from a congressional report into 9/11.

The pages reignited speculation over links that at least a few of the attackers had to Saudis, including government officials. The allegations were never substantiated by later US investigations.