Alexei Pushkov, chairman of the foreign affairs committee in the Duma, the lower house of parliament, said Russia would hit back after a suggestion by British Prime Minister David Cameron that the EU should restrict the movement of ruling politicians in protest at the de-facto annexation of Crimea.
"Of course, Russia would respond with the same measures," Pushkov was quoted as saying by Russian news agencies.
This would amount to "an unprecedented freezing of inter-parliamentary relations" and would interfere with the work of international organisations like the Council of Europe and the OSCE, he said.
But, added Pushkov, if the EU decides to freeze contacts with Moscow, Russia will simply build relations elsewhere.
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"Parliamentarians will develop links with other lawmakers outside Europe. It is only 28 countries; the world is not only the EU," he said.
Europe and the United States say Sunday's referendum in Crimea on independence from Ukraine is illegal, and have called on Russia to withdraw forces from the peninsula, on pain of diplomatic sanctions.
On Monday, Cameron told lawmakers the EU was looking at "further measures, the so-called second phase, which would need to start rapidly" if Russia failed to cooperate.