By Patricia Zengerle

WASHINGTON, Sept 27 (Reuters) - Opponents of a bill that would allow lawsuits against Saudi Arabia's government over the Sept. 11 attacks kept up their fight against the measure on Tuesday, a day before the U.S. Senate is expected to oppose President Barack Obama's veto, allowing the bill to become law.

Opponents circulated a letter from Ash Carter, Obama's Secretary of Defense, saying that the "Justice Against Sponsors of Terrorism Act," known as JASTA, posed risks for U.S. forces abroad.

"While we are sympathetic to the intent of JASTA, its potential second- and third-order consequences could be devastating to the Department and its Service members and could undermine our important counterterrorism efforts abroad," Carter wrote to Representative Mac Thornberry.

As Reuters reported on Friday, Thornberry, chairman of the House Armed Services Committee, has circulated a letter to his fellow House of Representatives Republicans saying that he will vote to sustain Obama's veto and urging them to do the same.

Obama vetoed the legislation on Friday. If Congress gets enough votes to override the veto for the first time since Obama became president in 2009 the bill would become law.

It takes two-thirds majorities in both the Senate and House to override a veto.

The legislation passed the Senate and House without opposition, in reaction to long-running suspicions, denied by Riyadh, that the hijackers of the four U.S. jetliners that attacked the United States in 2001 were backed by the Saudi government.

Fifteen of the 19 hijackers were Saudi nationals.

While a few lawmakers have expressed concerns about the implications of the bill, it still has strong support, among both Republicans and Obama's fellow Democrats.

Nancy Pelosi, the House Democratic leader, told reporters on Tuesday she would vote to override.

She said the vote was about giving a day in court to survivors and relatives of victims of the 2001 attacks, not a rebuke of Obama. "It isn't anti-president," she said.

(Additional reporting by Richard Cowan; Editing by Sandra Maler) ((patricia.zengerle@thomsonreuters.com, www.twitter.com/ReutersZengerle ; +1-202-898-8390; Reuters Messaging: patricia.zengerle.reuters.com@reuters.net))