Washington (CNN) The top two Republican leaders in Congress declined Tuesday to embrace a popular bill moving through the Senate that would allow families of 9/11 victims to sue Saudi Arabia.

House Speaker Paul Ryan expressed caution about unintended consequences of the legislation, which would clear the way for suits over Riyadh's alleged role in the terror attacks, and said the House would not rush the bill.

Senate Majority Leader Mitch McConnell, a Republican from Kentucky, was asked if he supports the bill and would put it on the floor.

He would only say he is "still looking" at it and that he doesn't have "any announcement to make."

The bill enjoys broad bipartisan support, but it has been stalled in the Senate by South Carolina Republican Lindsey Graham, an original co-sponsor.

He acknowledged to CNN that he has put a hold on the legislation as he tries to resolve concerns about late changes made to it.

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"I think we need to look at it," Ryan, a Wisconsin Republican, said in response to a question at a news conference. "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."

The bill, authored by Republican Sen. John Cornyn of Texas and Democratic Sen. Chuck Schumer of New York, would prevent Saudi Arabia and other countries accused of having terrorist ties from invoking their sovereign immunity in federal court.

The White House said Monday that President Barack Obama would likely veto the bill if Congress passes it.

Speaking to reporters, White House spokesman Josh Earnest warned that the bill would jeopardize international sovereignty and put the U.S. at "significant risk" if other countries adopted a similar law.

Saudi Arabia has long denied any role in the 9/11 attacks, but victims' families have repeatedly sought to bring the matter to court. In the past they've been rebuffed after Saudi Arabia has invoked legal immunity under current law.

Graham initiated his hold about a week ago after changes were made to the bill to resolve concerns of GOP Sen. Jeff Sessions of Alabama.

Graham said he wants to make sure the U.S. is not now held liable for the actions of some of the unsavory groups it is aligned with in the complex and shifting political environment of the Middle East.

"I want to make sure anything we do doesn't come back to bite us," said Graham.

While Saudi Arabia has never been implicated in the 9/11 attacks, 15 of the 19 hijackers were of Saudi descent. Moreover, there has long been suspicion about ties between the royal family of Saudi Arabia to al Qaeda, speculation that has only intensified as 28 pages of a congressional investigation into the 9/11 attacks remains classified.

Top senators and aides in each party said they were hopeful Graham's concerns could be quickly addressed and the bill would pass soon.

But following McConnell's lukewarm response to the bill -- and an already tight floor schedule with a variety of other proposals lined up for action -- it's not clear how soon or if the 9/11 measure might make it to the floor.

Senate Minority Leader Harry Reid said he supports the bill and the "pushback is coming from the Republicans."

"Now, I've spoken to the White House about this and a number of other issues. They don't particularly like it. But that's okay," the Nevada Democrat said. "I think we should move forward on this legislation and I hope we can."

Cornyn, the second-ranking GOP senator, blasted the White House for opposing the bill and accused the administration of wanting to prevent Senate passage before the President's high-profile meetings with Saudi leaders in Riyadh beginning on Wednesday.

"The President's attempts to derail this legislation that would help the victims of 9/11 pursue justice under the law is completely unacceptable," Cornyn said on the floor Tuesday. "Unfortunately, this shouldn't be a surprise. The President has steadfastly refused to declassify and release 28 pages of the 9/11 Commission report that pertain to allegations of Saudi Arabia's support for the 9/11 terrorists."

Ryan's hesitation presents a new problem for Cornyn and the bill's supporters.

"The speaker believes the legislation should be reviewed in regular order before decisions are made about the path forward," said Ryan aide AshLee Strong, suggesting the measure may not move quickly through the House even if the Senate approves the bill.

Cornyn said he hopes to discuss Ryan's concerns with him.

"I'd be happy to talk to him about it," Cornyn said. "It's very narrowly tailored and I think some people might be surprised that we've actually had exceptions to sovereign immunity in the past and this just carves out another very narrow one for terrorist attacks that occur on our soil. This isn't some open-ended bill."