Senate Majority Leader Harry Reid (D-Nev.) vowed to move forward with a controversial online piracy bill on Sunday, despite the White House expressing concern with the measure.

“We need to work on this and we’re going to—I will hope we can have a manager’s amendment when we get back here in a week or 10 days and move forward on this,” Reid told David Gregory on NBC’s “Meet the Press.”

“It’s important that we try to do this on a fair basis, and I’m going to do everything I can to get that done,” Reid said.

{mosads} He acknowledged that the bill has come under intense fire from consumer groups and Web companies including Google and Facebook, who say it would stifle innovation and censor free speech.

“I think they’re right, I think it could create some problems,” Reid admitted, but he expressed confidence that an amended version of the bill could be a “winner for everyone, not just for the content people.”

The Senate’s Protect IP Act and its House counterpart, the Stop Online Piracy Act (SOPA), are designed to go after foreign websites that offer illegal copies of music, movies and TV shows with impunity.

The bills 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.

In a statement on Saturday, senior White House officials said they would oppose any piracy law that “reduces freedom of expression, increases cybersecurity risk, or undermines the dynamic, innovative global Internet.”

In particular, the officials criticized a provision that would require Internet service providers to block infringing websites through a process known as Domain Name System filtering.

Sen. Patrick Leahy (D-Vt.), the sponsor of Protect IP, said last week that he is open to making changes to the site-blocking provision. Rep. Lamar Smith (R-Texas) said on Saturday that he plans to drop the provision from the House bill.

Despite expressing some concerns, the White House statement emphasized the administration’s commitment to passing a tough new anti-piracy law this year.

“While we are strongly committed to the vigorous enforcement of intellectual property rights, existing tools are not strong enough to root out the worst online pirates beyond our borders,” the officials wrote.

Reid said he has been working closely with Sen. Dianne Feinstein (D-Calif.) on crafting the anti-piracy measure.

“She’s got the eye of the storm in California because that’s where a lot of the theft of music and movies is taking place and also where Google and Facebook is headquartered,” he said.

The Senate is scheduled to vote on Protect IP on Jan. 24.

The status of SOPA is unclear. Rep. Smith, who chairs the House Judiciary Committee, has promised to push ahead with the bill, but Rep. Darrell Issa (R-Calif.) said Majority Leader Eric Cantor (R-Va.) has promised him the House will not vote on it unless there is a “consensus” on the bill.