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.