The controversial provision would have required service providers to block access to foreign Web sites accused of intellectual piracy, IDG News reported Saturday.
A similar provision was removed last week from the Senate version of the bill, sponsored by Sen. Patrick Leahy, D-Vt.
Smith, echoing concerns cited by Leahy, said that there has been widespread response to the provision and that it needed review.
In a statement, he said, "We will continue to look for ways to ensure that foreign Web sites cannot sell and distribute illegal content to U.S. consumers."
Arguments against the provision say it would jeopardize free speech. Proponents say that something must be done to protect U.S. intellectual property and copyrights.
Smith said the Stop Online Piracy Act, SOPA, was needed to protect "American companies from foreign online criminals who steal and sell American goods to consumers around the world."
But Sherwin Siy, deputy legal director of Public Knowledge, a digital rights watchdog group, said the two bills, including Leahy's Protect IP Act -- referred to as PIPA -- were "overbroad in their reach."
"Both bills still include a private right of action with few protections from abuse, meaning that sites can be killed without ever being proven to violate copyright."
The White House weighed in, as well. With input from Victoria Espinel, coordinator of Intellectual Property Enforcement at the Office of Management and Budget, Aneesh Chopra, U.S. chief technology officer, and Howard Schmidt, special assistant to the president and cybersecurity coordinator for the National Security Staff, the White House said the "important task of protecting intellectual property online must not threaten an open and innovative Internet."
The administration would not support a bill that "increases cybersecurity risk or undermines the dynamic, innovative global Internet," the White House said in a statement.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'