Melkonian first gained national recognition in 1957, winning a prize at the Contemporary Iranian Artist Exhibition of the Iran American Society. This was followed by the Imperial Court Prize at the Tehran Biennale in 1958 and first prize at the Paris Biennale in 1959. One of the artist's works was recently exhibited in London at the Victoria and Albert Museum, Epic Iran exhibition held from the 13 February to 12 September 2021.