Attempts by courts and officials in several countries to remove the clips have revived the debate over freedom of expression.
The judge in the Brazilian case acknowledged that banning content from sites like YouTube is a thorny issue, according to excerpts of the ruling cited in the National Union of Islamic Entities' statement.
"This type of jurisprudence cannot be confused with censorship," Miranda is quoted as writing. In the excerpts, the judge defines censorship as "the undue restriction of the civic consciousness."
YouTube routinely blocks video in specific countries if it violates laws there. It also removes video deemed to infringe copyrights, show pornography, contain hate speech or violate other guidelines. However, none of those restrictions had been applied in Brazil to the "Innocence of Muslims."
Google is now selectively blocking the video clips in countries that include Libya and Egypt. Google has said it made the decision to block the video in such places due to "the sensitive situations" there.
Galperin of the Electronic Frontier Foundation questioned whether a ban was really necessary in Brazil, which has seen no protests or rioting that have swept the Muslim world in recent weeks.
"The notion that there's a need to take it down to prevent violence is ludicrous," she said.
Miranda's ruling came on the same day that Brazilian President Dilma Rousseff addressed the United Nations and urged an end to prejudice against Muslims.
Google has said it has been so inundated by requests from governments worldwide to remove online content that it has begun releasing a summary of the demands, most relating to legitimate attempts to enforce laws on issues ranging from personal privacy to hate speech.
But Google, which has been locked in a high-profile battle with China's leaders over online censorship in the communist nation since 2010, says it increasingly fields requests from government agencies trying to use their power to suppress political opinions and other material they don't like.
Brazilian government agencies alone submitted a total of 194 content-removal requests during the final half of last year, according to a summary released by Google in June. Running just behind that was the United States, where police, prosecutors, courts and other government agencies submitted 187 requests to remove content over the same period.
Brazil and other parts of Latin America are crucial to Google's growth strategy. Company executives have said that Latin America is the country's fastest-growing market.
AP Technology Writer Michael Liedtke in San Francisco contributed to this report.
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