(CNN) -- Some lawmakers are rethinking their support of controversial anti-piracy bills that led to some websites shutting down in protest.
The protest was in response to the Stop Online Piracy Act (SOPA) bill, a piece of proposed legislation that is working its way through Congress. A Senate committee approved a similar bill in May called the Protect IP Act (PIPA), which is now pending before the full Senate.
The protest seemed to change the minds of lawmakers, including those that had strongly backed the bills in the past.
"We can find a solution that will protect lawful content. But this bill is flawed & that's why I'm withdrawing my support. #SOPA #PIPA," Republican Sen. Roy Blunt wrote on his official Twitter page.
Republican Sen. Marco Rubio of Florida, who was an initial co-sponsor of PIPA, reversed his position.
"I have decided to withdraw my support for the Protect IP Act. Furthermore, I encourage Senator Reid to abandon his plan to rush the bill to the floor. Instead, we should take more time to address the concerns raised by all sides, and come up with new legislation that addresses Internet piracy while protecting free and open access to the Internet," Rubio wrote on a Facebook post.
Rep Lee Terry, R-Nebraska, an original co-sponsor of SOPA, also said he had changed his view.
"Thank you for your concern about #SOPA. I have asked to have my name removed from the bill. However, the economic impact of IP theft is real and a solution is needed," Terry wrote on Facebook.
Later Thursday, Senate Republican Leader Mitch McConnell of Kentucky joined the newly minted opponents of the bill. He had not previously voiced an opinion on the legislation.
"While we must combat the online theft of intellectual property, current proposals in Congress raise serious legal, policy and operational concerns," McConnell said in a news release. "Rather than prematurely bringing the Protect IP Act to the Senate floor, we should first study and resolve the serious issues with this legislation."
Wikipedia, one of the websites that shut down on Wednesday, returned Thursday with the message: "Thank you for protecting Wikipedia. We're not done yet."
Clicking on that message takes a Wikipedia viewer to a thank you letter and instructions on how to continue fighting against anti-piracy bills that critics say could amount to censorship.
"Your voice was loud and strong," the message said. "Millions of people have spoken in defense of a free and open Internet." (Why Wikipedia went down at midnight)
On Wednesday, instead of the usual encyclopedia articles, visitors to Wikipedia's English-language site were greeted by a message about the decision to black out its Web page for an entire day. However, users were able to access its mobile site on some smartphones.
Boing Boing, a blog that took part in Wednesday's online protest but returned on Thursday, said the U.S. Senate was considering legislation that would "certainly kill us forever. The legislation ... would put us in legal jeopardy if we linked to a site anywhere online that had any links to copyright infringement."
"In the past, the media industry has often gone after particular infringers -- people who have downloaded stuff off the Internet and sharing it. And now they're going after websites that link to these things," Rob Beschizza, Boing Boing's managing editor, said Wednesday. "The bill is supposed to let copyright holders get court orders against them, and there's all sorts of various measures for getting sites blacklisted or blocked.
"The problem is that the measures are so wide-ranging and so open to abuse that we're worried that sites like ours could be brought down by frivolous claims," he said.
While not blacking out its home page, search giant Google joined the cause by covering its famous logo with a black rectangle and urging visitors, "Tell Congress: Please don't censor the web!"
SOPA's supporters -- including CNN's parent company, Time Warner, and groups such as the MPAA -- say that online piracy leads to U.S. job losses because it deprives content creators of income.
The bill's supporters dismiss accusations of censorship, saying the legislation is meant to revamp a broken system that doesn't adequately prevent criminal behavior.
But SOPA critics say the bill's backers don't understand the Internet's architecture, and therefore don't appreciate the implications of the legislation they're considering.
The controversy over SOPA and PIPA has turned into an all-out war between Hollywood and Silicon Valley. Media companies have united in favor of the bills, while tech's power players are throwing their might into opposing them. (Hundreds turn out for SOPA protest in New York)
"Both SOPA and PIPA are threats not just to the U.S. economy, and not just to all the jobs that this tech sector creates, but if they had existed, Steve Huffman and I could have never founded Reddit," said Alexis Ohanian, who co-founded the site. Millions visit Reddit to submit interesting links from websites, discuss them and vote on them, he said, calling it "sort of a democratic front page of the web." Reddit also went dark Wednesday morning and was back Thursday.
One member of Congress, Rep. Darrell Issa, R-California, who opposes the bills, said the unprecedented blackouts had "turned the tide against a backroom lobbying effort by interests that aren't used to being told no."
Issa is pushing for consideration of his own plan, the OPEN Act, addressing the matter. (OPEN Act: An experiment in digital democracy)
CNN's Ed Payne, Julianne Pepitone, John D. Sutter, Ted Barrett and Deirdre Walsh contributed to this report.