Brussels said that Stop Vivisection's European Citizens' Initiative (ECI) had passed the threshold of one million names from seven countries needed for the European Union to take up an issue.
The European Commission, the executive arm of the 28-member bloc, said it would now invite the organisers to "explain their ideas" within the next three months.
The European Parliament, the EU's only elected body, will then hold a public hearing.
"Then the Commission must decide whether it will act by adopting legislation, act in some other way to achieve the goals of the ECI, or not act at all," the Commission said.
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Instead, the group wants an outright ban on animal experimentation.
According to EU figures for 2011, around 11.5 million animals underwent tests for scientific purposes.
The commission said the petition won support in Finland, France, Germany, Hungary, Italy, Poland, Slovakia, Slovenia and Spain.