Congressional support for two anti-Internet piracy bills wavered yesterday after some of the Web’s biggest sites launched an online protest that triggered a flood of calls and tweets against the legislation.

The offices of Democratic representatives Ed Markey of Malden and Jim McGovern , a Worcester Democrat, said they busily fielded calls yesterday, nearly all in opposition to the bills. Of the 90 calls that McGovern’s office received by yesterday afternoon, for example, just one supported the legislation. In an online statement, McGovern called the bills unwise and unfair in their current form.

Key backers of the legislation dropped their support yesterday in the wake of the protests. Senator Orrin Hatch, a Utah Republican who cosponsored the Senate bill, said the legislation needs a deeper look. “Rushing something with such potential for far-reaching consequences is something I cannot support,’’ he said in a statement.

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Missouri Republican Senator Roy Blunt, another cosponsor of the bill, dropped his backing yesterday and called the legislation “deeply flawed.’’

Despite the response, protesting sites warned that it was too early to tell whether the bills are dead.

“This is far from over,’’ said Ivan Sigal, executive director of Global Voices, a Web community of international bloggers that grew out of Harvard University’s Berkman Center for Internet & Society.

Global Voices joined thousands of other websites - including the resource site Wikipedia, search giant Google, and online marketplace Craigslist - that shut down or posted online protest messages yesterday in an unusual show of unity for the fractured Internet industry.

Ethan Zuckerman, director of the Massachusetts Institute of Technology Center for Civic Media, said MIT’s Media Lab joined the protest - placing the message “Taking a stand against SOPA and PIPA’’ on its home page - because it “seemed like one of the moments when the Internet as a whole realized there was a threat to its very existence.’’

Many of the protesting sites directed users to contact their congressional representatives and express opposition to the Stop Online Piracy Act, the bill being considered in the House of Representatives, and the Protect Intellectual Property Act, the Senate version.

Both bills would allow copyright holders to seek court orders forcing websites to block illegal content such as unlicensed movies, music, and TV shows. The potential torrent of court orders presents a daunting prospect for sites that link to content created by others, such as Google and social media sites like Facebook, which also oppose the bills.

The legislation, which has had bipartisan support in Congress, is supported by a coalition of media organizations, including the Motion Picture Association of America and the Recording Industry Association of America. Proponents say the legislation is needed to fight online piracy.

Supporters called it an abuse of power that some of the Web’s most popular sites used their influence to stump on a political issue yesterday.

“It’s a dangerous and troubling development when the platforms that serve as gateways to information intentionally skew the facts to incite their users and arm them with misinformation,’’ Jonathan Lamy, spokesman for the music industry group, wrote in an e-mail.

An early version of the antipiracy legislation would have forced US Internet providers and search engines like Google and Yahoo to block foreign websites with illegal material. Lawmakers modified some of those provisions, but the changes did not appease opponents.

One of the most visible participants in yesterday’s protest was Wikipedia. When users visited the English version of the online encyclopedia, the screen went dark and a protest message appeared. There did appear to be several ways to access the online encyclopedia, however, including via its site meta.wikimedia.org and through the version of Wikipedia designed for smartphones.

Evan Hansen, editor of the Wired.com, which blacked out its online headlines yesterday, said he was not surprised by the protest or the response.

“The history of the Web community comes out of a libertarian perspective,’’ he said, “and oversight and government intervention into these new communities is viewed skeptically.’’