In the unprecedented legal action, comprising nine separate cases brought before the ICJ at The Hague, the Republic of the Marshall Islands accused the nuclear weapons states of a "flagrant denial of human justice".
The Marshall Islands, an island country located in the northern Pacific Ocean, argued that it is justified in taking the action because of the harm it has suffered as a result of the nuclear arms race.
In the lawsuit, Marshall Island said that the five original nuclear weapon states - US, Russia, UK, France and China - are continuously breaching their legal obligations under the treaty.
The lawsuits contend that all nine nuclear-armed nations are violating customary international law.
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Article VI of the Non-Proliferation Treaty (NPT) requires states to pursue negotiations "in good faith" on cessation of the nuclear arms race "at an early date" and nuclear disarmament.
The four newer nuclear-armed states - Israel, India, Pakistan, and North Korea - are not party to the treaty but are bound by these nuclear disarmament provisions under customary international law.
"Our people have suffered the catastrophic and irreparable damage of these weapons and we vow to fight so that no one else on earth will ever again experience these atrocities," Marshall Islands Foreign Minister Tony de Brum said.
"The continued existence of nuclear weapons and the terrible risk they pose to the world threaten us all," he said.