Protesters carrying signs that read "No to Censorship" and "Freedom of Expression" walked along Mexico City's main Reforma Avenue on their way to the Senate building yesterday after organising the demonstration on social networks.
The government says the proposal seeks tools to combat illegal activities on the Internet, including child pornography.
One of the most controversial articles in the law allows the government to request that internet providers "block access to certain content, applications or services," including cutting off cellphone service or Internet access if it considers there is a risk to public safety.
In recent years, social networks have served as the main sources of information in many parts of Mexico affected by drug violence because mainstream media has stopped sending reporters there because of security fears.
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Carlos Brito, a graduate student and member of the Network in Defense of Digital Rights, said the law could lead telecommunication companies to impose limits on Internet access to avoid being accused of promoting illegal acts.
Deputy Communications Secretary Jose Ignacio Peralta posted on Twitter that the law aims to punish those who use it for illegal purposes.
"It doesn't oppose a free Internet," Peralta wrote on Twitter.