Sung Kim, US Special Representative to North Korea, made the warning days after Pyongyang test-launched a record eight ballistic missiles on Sunday.
Any such nuclear test would be met with a “swift and forceful response”, US Deputy Secretary of State Wendy Sherman told reporters.
Pyongyang has not carried out a nuclear test for five years.
However, tensions have been rising on the Korean peninsula. Speaking from Jakarta, Mr Kim said North Korea had tested an unprecedented number of missiles this year – 31 compared to 25 during the whole of its last record-breaking year, 2019.
“And it’s only June,” he told reporters during a briefing in Jakarta, Indonesia.
He added that rhetoric used by North Korean officials had suggested a willingness to use tactical or small-sized nuclear weapons as well.
When asked by reporters when the next round of testing would take place, Mr Kim warned it could happen “any time” – including as early as this week, according to news outlet Bloomberg.
Meanwhile, Ms Sherman told reporters in Seoul – where she has been meeting with South Korean and Japanese officials – that any such test “would be in complete violation of UN Security Council resolutions”.
“I believe that not only ROK (South Korea) and United States and Japan but the entire world will respond in a strong and clear manner,” she said.
North Korea is yet to respond to the US assertions.
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However, the US – which, with its ally, South Korea, responded to Pyongyang’s recent launches by launching eight missiles in response on Monday – remained committed to engaging diplomatically with North Korea “without preconditions”, Mr Kim said.
He went on to say the message had been conveyed “through private channels”. The US had also offered proposals on humanitarian cooperation and assistance with the recent Covid-19 outbreak in North Korea, he said. The country has been grappling with the spread of the virus in an unvaccinated population of nearly 25 million.
“However, to date, the DPRK has not responded and continues to show no indication that it is interested in engaging,” he said.