Staff at the group, Memorial, said armed and masked state investigators raided its offices in Russia's second city on December 4 and seized computers and documents.
Among material seized was a history of political repression in the Soviet Union and a computer-based tour of Stalin-era forced work camps or gulags, the organization said.
A statement from the French EU Presidency said the raid, days before the 60th anniversary of the Universal Declaration of Human Rights, "sends out a negative signal."
It said the work of the group to safeguard the memory of Stalin's victims and protect human rights were internationally recognized and acclaimed.
"The European Union urges the Russian authorities to guarantee the freedom of action of this organization...It is very concerned at the use of the law on extremism against this association," the statement said.
At the time of the raid, a spokesman for the Russian prosecutor-general's main investigative unit was quoted by Interfax news agency as saying the search was part of a probe about a local newspaper article.
Other rights groups said the raid was intended to demonstrate the power of the authorities and to show who was boss in the country.