It was on August 6 and 9 in 1945 that America had dropped bombs on Hiroshima and Nagasaki respectively.
But Japan, together with the world's nuclear weapon states and other countries under the U.S. umbrella have recently refused to participate in the United Nations treaty.
A number of speakers also talked about the United Nations last month adopting an global treaty banning nuclear weapons.
In light of the Constitution, Hiroshima calls on the government to do all it can to bridge the gap between the nuclear weapon states and those that do not have such weapons to facilitate the treaty's ratification.
Hiroshima's appeal of "never again" on the anniversary of the world's first atomic bomb attack has acquired renewed urgency as North Korea moves ever closer to acquiring nuclear weapons.
The anniversary comes amid growing concern in Japan over North Korea's recent missile tests, and mounting tension over its nuclear programme. You could find yourself suffering their cruelty.
He warned against the stockpile of 15,000 nuclear weapons and unsafe rhetoric regarding their use.
He referred to the adoption in July 2017 of the treaty on the prohibition of nuclear weapons by United Nations member states as a positive development.
In the city's annual peace declaration, Matsui pointed out that it is time to "strive to advance further towards a nuclear-weapon free world".
"The states possessing nuclear weapons have special responsibility to undertake concrete and irreversible steps on nuclear disarmament", Guterres stressed.
Many in Japan feel the attacks on Hiroshima and Nagasaki amounted to war crimes and atrocities because they targeted civilians, and also because of the unprecedented destructive nature of the weapons.