The draft resolution, submitted by liberal and green political groups on Wednesday, called "authoritarian tendencies" in Russia a "part of a worrying trend" that threatened the country's "democratic development and the legitimacy of the Russian leadership."
The document listed a number of issues of "serious concern", including human rights, democracy, freedom of expression and civil society rights.
However, the two main political groups in the parliament - the conservatives and the socialists - said there was "nothing new to say," and "repeating the same things for no particular reason would not be productive".
The decision comes ahead of an EU-Russia summit in Mafra, in Portugal, on October 26.
Friday's summit is to address major issues in EU-Russian relations, including a new partnership and cooperation agreement, the EU, domestic Russian issues of concern to Europe, the issues of international importance, mainly Kosovo and Iran, and U.S. plans for the deployment of its missile shield elements in Europe.
