Ukraine is marking this week 1,020 years since Christianity was adopted in Kievan Rus, with church services, processions, and other events to mark the anniversary.
The lawmaker in question, Konstantin Zatulin, was detained at Simferopol airport in the Crimea in the south of Ukraine on Thursday. He flew back to Moscow later on Friday, the agency reported.
"According to our information, the SBU filed criminal charges after receiving information that Zatulin and Kirill Frolov, a representative of the Institute of CIS Countries, had attempted to destabilize the situation [in Ukraine] during the celebrations for the 1020th anniversary of Christianity in Kievan Rus," the agency reported.
On Wednesday, Zatulin criticized appeals for the unification of the country's Orthodox churches by Ukrainian President Viktor Yushchenko, who the MP said sought to separate the Ukrainian Church from the Moscow Patriarchy.
The Russian Foreign Ministry has summoned the Ukrainian ambassador to explain the refusal to allow Zatulin into Ukraine.
Russia's Foreign Ministry said in a statement that the refusal was "a flagrant manifestation of an unfriendly attitude toward a prominent public figure and member of the Russian parliament."
Zatulin, along with outspoken fellow MP, Vladimir Zhirinovsky, was earlier listed as a persona non grata by Ukrainian authorities after his involvement in 2006 protests in the Crimea against joint NATO-Ukraine Sea Breeze military exercises in the Black Sea. He also called the presence of U.S. troops in Crimea "illegal under Ukrainian law."
Sea Breeze 2008 began last Monday in Ukraine's Odessa, Crimea and Black Sea coastal regions and has been hit by a series of protests and demonstrations.
Zatulin's persona non grata status was annulled however when Moscow and Kiev mutually scrapped lists of "undesirables" in 2007.