The US, Britain and France were among the countries that skipped a UN meeting to discuss a new treaty.
More than 120 others endorsed a plan for a legally binding nuclear ban.
But US envoy Nikki Haley said national security required nuclear arms because of "bad actors" who could not be trusted.
"There is nothing I want more for my family than a world with no nuclear weapons. But we have to be realistic," she told reporters.
"Is there anyone that believes that North Korea would agree to a ban on nuclear weapons?"
North Korea has recently been testing nuclear and missile technology, despite warnings from the international community - including China.
The UN conference to negotiate a legally binding nuclear ban treaty was announced in October.
Britain, France, Israel, Russia and the United States voted "no" to the nuclear ban treaty back then, while China, India and Pakistan abstained.
Japan - the only country to have suffered atomic attacks, in 1945 - also voted against the talks.
Nobushige Takamizawa, Japan's ambassador to the UN, said working on a treaty "without the involvement of nuclear weapon states [would] only deepen the schism and division" in the international community.
On Monday, Ms Haley said: "In this day and time we can't honestly say that we can protect our people by allowing the bad actors to have them and those of us that are good trying to keep peace and safety, not to have them."
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Countries not attending, like the US and the UK, remain committed to the Non-Proliferation Treaty, which entered into force in 1970 and is aimed at preventing the spread of nuclear weapons and weapons technology.
But Swedish Foreign Minister Margot Wallstrom, whose country his leading the calls for a total ban "leading towards [nuclear weapons] total elimination", along with Austria, Ireland, Mexico, Brazil and South Africa, said she expected this would "take a long time".
"Let's not be naive," she said at the UN last week. "But it's very important in these days, when you see more of this rhetoric, and also sort of power demonstrations, including threatening to use nuclear weapons."
A worldwide nuclear ban is simply not "realistic", the US ambassador to the UN has said, as nearly 40 countries stayed away from talks on the subject.