WASHINGTON (Reuters) - The U.S. House of Representatives would override any presidential veto of a bill allowing survivors and families of victims of the Sept. 11 attacks to sue Saudi Arabia, Speaker Paul Ryan predicted on Wednesday while also citing concerns with the legislation.

"I worry about legal matters. I worry about trial lawyers trying to get rich off of this. And I do worry about the precedence. At the same time, these victims do need to have their day in court," Ryan, a Republican, told reporters.

Congress has overwhelmingly passed the Justice Against Sponsors of Terrorism Act in reaction to long-running suspicions, denied by Saudi Arabia, that hijackers of the four U.S. jetliners that attacked the United States in 2001 were backed by the Saudi government.

Obama in coming days is expected to veto the bill on grounds that other countries could use the law as an excuse to sue U.S. diplomats, service members or companies. But Congress could have the last word if the Senate and House of Representatives each override that veto by a two-thirds vote.

"I do think the votes are there for the override," Ryan said.

When asked by a reporter if U.S. support for Saudi Arabia was "unconditional," Ryan responded that the country "is a very important and valuable ally" and is helping Washington in the "war on terror."

He noted, however, "Our support for any country is not unconditional."

(Reporting By Richard Cowan; Editing by Andrew Hay)