Yevgeny Fyodorov from the ruling United Russia party said the 1991 resolution that led Vilnius to break from the USSR was "illegal."
The two countries want to expand their Union State to involve other countries, Belarusian media reported.
Russian television salutes the Soviet "red banner with yellow hammer and sickle and star" flying over Ukraine that once signaled the defeat of Nazi Germany.
Giuliani's ties to the former Soviet Union go back to the 1990s.
Diplomats from Ukraine and five other former Communist countries rallied for the U.S. Senate's backing.
After less than a year in office Mirziyoyev has called for dropping entry and exit visas.
The 29-year-old will soon be eligible to succeed his father.
Russia strongly protested the move to take down the Communist monument.
The group were also allegedly smoking in a no-smoking area.
Maardu marked May 9 with a ceremony honouring Soviet troops.
The Russian president also made no mention of allied anti-Nazi efforts.
Lenin was as popular as Prime Minister Dmitry Medvedev in a recent poll.
Russia's Foreign Ministry called a contest for the best response.
Russia has vowed a "highly effective" and "asymmetrical" response.