But Matsui also called on Japan itself to take the lead in working towards eliminating nuclear weapons.
"If the human family forgets history or stops confronting it, we could again commit a awful error", Matsui said in this year's peace declaration, read out at a ceremony to mark the 73rd anniversary of the bombing.
Abe said differences between the nuclear and non-nuclear states had widened, but he pledged to do more to bridge their gap.
More than 300,000 people across China were killed by Japan's biological weapons during WWII.
The anniversary comes amid hopes to denuclearize North Korea after President Donald Trump and North Korean leader Kim Jong Un made vague aspirational statements of denuclearizing the peninsula when they met in Singapore in June. It was the first use of nuclear weapons against human beings.
Despite such a tragedy, the ambassador said, he believes that people in Hiroshima do not have negative feeling toward the people of the country, which dropped the atomic bomb. The pact was adopted in July 2017.
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The US attack on Hiroshima ultimately killed more than 140,000 people; the bombing of Nagasaki ended another 70,000 lives three days later.
The mayor of Hiroshima said that while the thinking of the hibakusha is spreading throughout the world, some countries are proclaiming self-centered nationalism and modernizing their nuclear arsenals.
"Our nation, while maintaining our (non-nuclear weapons) principles, will patiently work to serve as a bridge between the two sides and lead efforts by the worldwide community" to reduce nuclear weapons, Abe said. In his speech this year, Abe said Japan will "make strenuous efforts to serve as a bridge between nuclear powers and non-nuclear states".
The United Nations secretary-general urged in his speech delivered by Izumi Nakamitsu, high representative for disarmament affairs, that hibakusha continue to exert their "moral leadership" for the world to seek the abolition of nuclear arms.
As of March, the number of hibakusha stood at 154,859. Their average age was 82.06, up 0.65 from a year before.
In Friday, Aug. 8, 2018, photo, Namio Matsura, 17-year-old member of the computation skill research club at Fukuyama Technical High School, watches Hiroshima city before atomic bomb fell in virtual reality experience at the high school in Hiroshima, western Japan.
Tomie Makita, 88, of Hiroshima pays a visit to the park every year on August 6 to remember the bombing that claimed the lives of her friends.