President Obama said he felt “deep sympathy” for the families but that the law would be “detrimental to US national interests”.
Saudi Arabia’s foreign minister had warned that the bill could cause his government to withdraw US investments.
The country denies any involvement in the 2001 attacks which killed nearly 3,000 people.
Fifteen of the 19 hijackers that targeted the World Trade Center and the Pentagon were Saudi citizens.
SOURCES: News Now/BBC News