UN Secretary General Antonio Guterres opened the event in NY while hailing the agreement as a milestone and the first multilateral pact on disarmament in more than two decades.
Dozens of countries signed a treaty to ban nuclear weapons on Wednesday amid tensions over North Korea's nuclear and missile tests, although the United States, Britain, France and others boycotted the event at the annual United Nations gathering of world leaders.
Nuclear powers argue their arsenals serve as a deterrent against a nuclear attack and say they remain committed to the nuclear Non-Proliferation Treaty (NPT).
The Treaty - adopted on 7 July this year at a United Nations conference in NY by a vote of 122 in favour to one against (Netherlands), with one abstention (Singapore) - prohibits a full range of nuclear-weapon-related activities, such as undertaking to develop, test, produce, manufacture, acquire, possess or stockpile nuclear weapons or other nuclear explosive devices, as well as the use or threat of use of these weapons.
"It will raise public awareness about the risks of nuclear weapons".
Earlier in the day, the Treaty on the Prohibition of Nuclear Weapons was opened for signature at the UN General Assembly in NY. "Therefore, there will be no change in the legal obligations on our countries with respect to nuclear weapons".
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North Korea has been subject to global condemnation for its development of nuclear weapons and ballistic missiles.
"You may recall that in the early 60s, France tested an atom bomb, a nuclear device in the Sahara and Nigeria broke up diplomatic relations with France".
"Nigeria has always been a strong advocate of de-nuclearisation of the world".
The signing ceremony came a day after President Donald Trump threatened to "totally destroy North Korea" if the United States is forced to defend itself or its allies.
Japan, the only nation ever to suffer nuclear attacks, did not sign the document out of deference to the US, on which the country relies for military protection.
The treaty will enter into force when 50 countries have ratified it. Only a few countries are expected to submit their ratification Wednesday.