Pictures released by the semi-official ISNA news agency showed S-300 missile tubes and radar equipment during a military parade in southern Tehran, the BBC wrote.
Iran insists the system is necessary to defend itself, but the U.S. and Israel have criticized the sale.
The controversial contract got the go-ahead after last year's deal to lift international sanctions on Iran.
Read alsoRussia delivers 1st batch of S-300 missile systems to IranSix world powers led by the U.S. agreed in July to lift the sanctions which had locked down much of Iran's economy for years, in exchange for limits on Tehran's nuclear program.
The missile parts went on display as President Hassan Rouhani pledged to defend Muslim countries against "terrorism and Israel" while insisting that his country's neighbors should not feel threatened.
The $800 million (GBP 562 million) missile contract, signed in 2007, was frozen by Russia in 2010 because of international sanctions against Iran. President Vladimir Putin unfroze it a year ago.
The S-300, made by Rostec, can be used against multiple targets including jets, or to shoot down other missiles.