WASHINGTON (Reuters) - Two senior U.S. senators said on Wednesday they want to amend a law allowing lawsuits against Saudi Arabia over the Sept. 11 attacks to narrow the scope of possible lawsuits.

Lindsey Graham and John McCain, two of the Republican party's congressional foreign policy leaders, said they would introduce an amendment to the law so that a government could be sued only if it "knowingly" engages with a terrorist organization.

"All we're saying to any ally of the United States (is), you can't be sued in the United States for an act of terrorism unless you knowingly were involved, and the same applies to us in your country," Graham said in a Senate speech.

In September, the Senate and House of Representatives overwhelmingly rejected President Barack Obama's veto of the Justice Against Sponsors of Terrorism Act, known as JASTA, making it U.S. law.

However, lawmakers said almost as soon as they did so that they wanted the scope of the legislation narrowed to ease concerns about its potential effect on Americans abroad, which was one reason Obama vetoed the measure.

The law grants an exception to the legal principle of sovereign immunity in cases of terrorism on U.S. soil, clearing the way for lawsuits seeking damages from the Saudi government. Riyadh denies longstanding suspicions that it backed the hijackers who attacked the United States in 2001.

However, it was not immediately clear whether Graham and McCain's proposal would go anywhere. A group of Sept. 11 families, who lobbied intensely for the bill and have strong support in Congress, immediately objected to their suggestion because it would weaken the law.

(Reporting by Patricia Zengerle; Editing by Jonathan Oatis)