News agencies quote the head of Russia's Federal Security Service and head of the government's antiterrorism committee, Nikolai Patrushev, as telling all citizens and officials to be on high alert.
He said he had ordered search operations and preventative action.
Russian Deputy Prime Minister and Defense Minister Sergei Ivanov also confirmed the alert.
"The Defense Ministry of the Russian Federation has taken additional measures to protect the most important military, state, and government facilities," Ivanov told journalists. "On the whole, the armed forces continue to operate in a normal mode."
In the past, radicals connected with the Chechen resistance have attacked Moscow's metro and other public places. Hundreds of hostages were taken in a theater siege in Moscow in October 2002 and at a school in Beslan, in the southern Russian republic of North Ossetia, in September 2004.
However, Russia has not seen a major terrorist incident outside of the North Caucasus in over two years.
Terror In Russia
An archive of RFE/RL's extensive coverage of terrorism in Russia.