WASHINGTON (AP) — The Senate's top Republican is warning that legislation enacted over President Barack Obama's veto to allow families of Sept. 11 victims to sue Saudi Arabia in U.S. courts may have "unintended ramifications" and that lawmakers should discuss fixes to the measure.

US Sen. Mitch McConnell prepares to speak at the Republican National Convention in Cleveland. Thomson Reuters WASHINGTON — The Senate's top Republican Thursday warned that legislation enacted over President Barack Obama's veto to allow families of Sept. 11 victims to sue Saudi Arabia in U.S. courts may have "unintended ramifications" and that lawmakers should discuss fixes to the measure.

Majority Leader Mitch McConnell, R-Ky., said the White House was too slow to warn about the "potential consequences" of the measure. Both the House and Senate overwhelmingly overrode Obama's veto of the measure on Wednesday.

McConnell said he told the president recently that the 9/11 victims bill "was an example of an issue that we should have talked about much earlier."

The legislation gives victims' families the right to sue in U.S. court for any role that elements of the Saudi government may have played in the 2001 attacks. Courts would be permitted to waive a claim of foreign sovereign immunity when an act of terrorism occurred inside U.S. borders. Supporters said the families of 9/11 victims should be able to pursue justice against Saudi Arabia for its alleged backing of the attackers.

But those concerned about the law warn that it could have a chilling effect on Saudi Arabia's cooperation with the U.S. in fighting terrorism. They also warn that it could trigger lawsuits from people in other countries seeking redress for injuries or deaths caused by military actions in which the U.S. may have had a role.

"Everybody was aware of who the potential beneficiaries were but nobody really had focused on the downside in terms of our international relationships," McConnell said.

McConnell said that the dynamic involving the bill — in which it barreled through both chambers before and proved unstoppable — was what happens when there is "failure to communicate early about the potential consequences of a piece of legislation that was obviously very popular."

Other top Republicans and Democrats such as Senate Foreign Relations Committee Chairman Bob Corker, R-Tenn., are already working on proposed fixes to the law.