House Oversight Chairman Darrell Issa (R-Calif.) said early Saturday morning that Majority Leader Eric Cantor Eric Ivan CantorThe Hill's Campaign Report: Florida hangs in the balance Eric Cantor teams up with former rival Dave Brat in supporting GOP candidate in former district Bottom line MORE (R-Va.) promised him the House will not vote on the controversial Stop Online Piracy Act (SOPA) unless there is consensus on the bill.

"While I remain concerned about Senate action on the Protect IP Act, I am confident that flawed legislation will not be taken up by this House," Issa said in a statement. "Majority Leader Cantor has assured me that we will continue to work to address outstanding concerns and work to build consensus prior to any anti-piracy legislation coming before the House for a vote."

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The announcement comes just hours after Judiciary Chairman Lamar Smith (R-Texas), SOPA's sponsor, made a major concession to the bill's critics by agreeing to drop a controversial provision that would have required Internet service providers to block infringing websites.

SOPA is designed to go after foreign websites that offer illegal copies of music, movies and TV shows with impunity. Even without the provision allowing sites to be blocked, the bill would empower the Justice Department and copyright holders to demand that search engines delete links to sites “dedicated” to copyright infringement. Ad networks and payment processors would be prohibited from doing business with the sites.

The bill has sparked a backlash from Internet freedom advocates and Web companies, including Google, Yahoo and Facebook, who say it would stifle innovation and suppress free speech.

The provision that would have required Internet providers to block infringing websites was one of the most controversial aspects of the bill. Google Chairman Eric Schmidt compared the provision to how China censors political speech online.

Issa, who is a former chairman of the Consumer Electronics Association, is close with the tech community and has been an outspoken critic of SOPA. He had scheduled a hearing for next Wednesday to examine the potential consequences of the bill's site-blocking provision, but he announced in his statement Saturday that he would cancel the hearing in light of Smith's decision to drop the provision.

Issa said that even without the site-blocking provision, the bill is "fundamentally flawed."

"Right now, the focus of protecting the Internet needs to be on the Senate where Majority Leader Reid has announced his intention to try to move similar legislation in less than two weeks," he said.

The Senate bill's sponsor, Sen. Patrick Leahy Patrick Joseph LeahyBipartisan representatives demand answers on expired surveillance programs Democrats shoot down talk of expanding Supreme Court Battle over timing complicates Democratic shutdown strategy MORE's (D-Vt.), said on Thursday that he is open to changes to the site-blocking provision.