President Obama has said Congress made a "mistake" by overriding his veto and pushing through a bill that allows legal action against Saudi Arabia over the 9/11 attacks.
He said the bill would set a "dangerous precedent" for individuals around the world to sue the US government.
Wednesday's vote was the first time Mr Obama's veto power was overruled.
CIA Director John Brennan agreed that the bill carried "grave implications" for national security.
He added: "The downside is potentially huge."
The Justice Against Sponsors of Terrorism (JASTA) legislation opens the door for victims' families to sue any member of the Saudi government suspected of playing a role in the 9/11 attacks.
Fifteen of the 19 hijackers were Saudi nationals, but the oil-rich kingdom - a key US ally - has denied any role in the attacks, which left nearly 3,000 people dead.
While US intelligence raised suspicions about some of the hijackers' connections, no link has been proven to support claims that Saudi officials provided financial support to the suspects.
Mr Obama told CNN on Wednesday: "It's a dangerous precedent and it's an example of why sometimes you have to do what's hard.
"And, frankly, I wish Congress here had done what's hard.
"The concern that I've had has nothing to do with Saudi Arabia per se or my sympathy for 9/11 families.
"It has to do with me not wanting a situation where we're suddenly exposed to liabilities for all the work that we're doing all around the world and suddenly finding ourselves subject to private lawsuits."
Mr Obama suggested that his colleagues' voting patterns were influenced by political concerns.
"If you're perceived as voting against 9/11 families right before an election, not surprisingly, that's a hard vote for people to take.
"But it would have been the right thing to do."
The Senate voted 97-1 and the House of Representatives 348-77, meaning the bill becomes law.
White House spokesman Josh Earnest told reporters the vote was "the single most embarrassing thing the United States Senate has done" in decades.
But the measure's supporters contended the legislation only applies to acts of terrorism that have occurred on US soil - and side-swiped at Mr Obama for his perceived prioritising of relations with Saudi Arabia.
"The White House and the executive branch (are) far more interested in diplomatic considerations," said Democratic New York Senator Chuck Schumer.
"We're more interested in the families and in justice."