The petition was presented by representatives of Avaaz, an organization that uses the internet to mobilize support for various political issues.
"We call on you to stand for a free and open Internet and reject the ratification of the Anti-Counterfeiting Trade Agreement (ACTA), which would destroy it," the petition said.
Proponents argue that ACTA would change nothing in European Union law and would be a means of extending to other countries the kinds of protections against counterfeit goods and copyright infringement the EU already offers. They argue the treaty would protect European consumers against such dangers as counterfeit drugs and auto parts, and European businesses against having to compete with cheap and illegal imitations of their goods.
The International Trademark Association, which represents thousands of companies, argues the agreement would "create and preserve millions of European jobs" and "spur European economic recovery, competitiveness and growth."
The treaty would also provide a framework for the enforcement copyright law, protecting writers, composers and performers from having their work distributed without permission or compensation.
It says countries could have their authorities order an online service provider to disclose identifying information about a subscriber whose account had been allegedly used for trademark or copyright infringement.
Fears that individual Internet users would be targeted prompted protests in several European cities in early February.
The treaty's supporters say there is no intention to go after individuals, only large-scale users making money off libraries of material they make available for illegal download.
But David Martin, the member charged with shepherding the treaty through the European Parliament, said Tuesday he thought there were serious problems with what he called the vagueness of the text.
"I have no interest, in the process, in criminalizing individual consumers," he said. "I think you have to distinguish between the consumer and the producer of illegal content. I have no interest in the teenager sitting in his room deciding to download a piece of music for free because he finds there's an internet service, that there's a site providing that music for free."
In any event, the effort to have the European Union ratify the treaty has for the time being come to a screeching halt. EU passage would require ratification by each of the 27 member countries.
As opposition to the treaty grew in some countries recently, the European Commission, the EU's executive branch, suspended efforts to get the treaty ratified and decided to send the text instead to the European Court of Justice to see whether the agreement would violate any fundamental EU rights.
Martin said the Parliament might send its own questions to the court, as well. He and other observers said they expected the court's assessment to take a year or more to complete.
Eminia Mazzoni, chairwoman of the Parliament's Petitions Committee, said she welcomed the petition.
"Receiving a petition supported by more than 2 million people places an even bigger responsibility on us to listen to the European people and offer them a place to express their views to the European institutions," she said.
Mazzoni said she had also received letters and organizations in favour of ACTA.
Don Melvin can be reached at http://twitter.com/Don_Melvin