There were similar vows made by anti-nuclear activists at other events marking the anniversary, including in the United States.
In the city of Hiroshima Monday, about 40,000 survivors, residents and visitors from around the world observed a moment of silence as they gathered in the Peace Park built at the dead center of where the bomb was dropped on August 6, 1945, by the U.S. B-29 bomber Enola Gay.
An estimated 140,000 people were killed instantly or died within a few months after the bombing. Three days later, another U.S. airplane dropped a plutonium bomb on the city of Nagasaki, killing about 80,000 people.
"Japan has been taking the path toward global peace for 62 years since World War II. The tragedies of Hiroshima and Nagasaki should never be repeated in any place on Earth," said the Japanese prime minister, in a speech at the Hiroshima ceremony.
"We will take an initiative in the international community and devote ourselves wholeheartedly toward the abolition of nuclear weapons and realization of peace," Abe said.
The mayor of Hiroshima took an even stronger stand, combining his anti-nuclear stance with criticism of the United States.
"The Japanese government must humbly learn the atom bomb victims' reality and philosophy, and they are responsible for sending out the message to the world," said Hiroshima Mayor Tadatoshi Akiba. "The Japanese government should comply with the nation's pacifist Constitution as it is and clearly say no to wrong and outdated policies of the United States."
This year's memorial comes at a particularly sensitive time for Japan.
Following North Korea's first nuclear test explosion last Oct. 9, some prominent Japanese politicians have suggested Tokyo should at least debate development of nuclear weapons. Their remarks prompted Abe and other top officials to state Japan will not stray from its three long-standing principles of not possessing, developing or allowing nuclear weapons on Japanese soil.
Last month, Defense Minister Fumio Kyuma resigned amid a public outcry over his having suggested that the U.S. atomic bombings may have been justified.
Abe reiterated Monday that Japan will remain committed to the country's non-nuclear principles.
"We promise that we will comply with provisions of the Constitution, sincerely seek global peace, and adhere to the three non-nuclear principles," he said.
In a message marking the anniversary, U.N. Secretary-General Ban Ki-moon said nuclear proliferation is "one of the most pressing problems confronting our world."
"Today our challenge ... is to make the world safer for succeeding generations. This requires us to continue to work toward a world free of nuclear dangers, and ultimately, of nuclear weapons," Ban said in the message, delivered by Sergio de Queiroz Duarte, the U.N.'s high representative for disarmament affairs.
There are about 252,000 survivors of the attacks, according to the health ministry. Many have developed various illnesses caused by radiation exposure, including cancer and liver diseases.
Abe, in a meeting of survivors on Sunday, proposed a plan to relax some screening requirements so that more victims can get extensive medical support from the government. Currently only a restricted number of bomb victims meet the criteria for receiving special medical aid.
Ceremonies will also be held on Thursday's anniversary of the Nagasaki attack.
Japan surrendered on Aug. 15, 1945, bringing World War II to an end.