Accepting the stone at a ceremony in his office, the Croatian president said that the world was still facing numerous challenges, including terrorism and inequality, as potential threats to peace.
"The Peace Stone is a memento of the past, but also a warning of what the future might be like. Croatia is a consistent advocate of a future of peace, security, stability and equality," Mesic said.
The Peace Stone will be displayed at the newly-built Museum of Modern Art in Zagreb.
"I wish that a look at the stone would awaken the consciousness of the need for a constant fight for peace, because peace is a value no one will give us as a gift, but we have to fight for it all the time," Mesic.
The Hiroshima Stone is a granite slab measuring about 50 centimetres in height and 50 kilograms in weight. Hiroshima's streets were cobbled with such stones when an atomic bomb was dropped on the city on August 6, 1945.
The stone brought to Croatia is one of the 188 stones that were dug from under tram tracks near the Aioi bridge, located some 200 metres north of the explosion site. Each stone is engraved with the image of Kannon, the Japanese goddess of mercy.
Hiroshima peace stones are presented to heads of state or government with a view to promoting the idea of peace among the nations of the world.
Since the establishment of the Stone for Peace association in May 1991, some 100 countries have received such stones and put them on public display.