The US is "ready to talk any time" with North Korea without preconditions, says Secretary of State Rex Tillerson.
His statement appeared to shift the US position away from previous demands that North Korea must disarm before any talks can be held.
"Let's just meet and let's talk about the weather if you want," he told a policy forum in Washington DC.
North Korea's pursuit of nuclear weapons technology has led to heavy US-led sanctions against the regime.
Separately, the UN's political chief Jeffrey Feltman, who recently visited Pyongyang, told reporters that North Korean officials felt it was "important to prevent war".
Diplomatic relations between the US and North Korea have been strained by recent North Korean nuclear and missile tests, and by a war of words between US President Donald Trump and North Korea's leader Kim Jong-un.
Speaking at the Atlantic Council policy forum on Tuesday, Mr Tillerson said the US "simply cannot accept a nuclear armed North Korea".
But appearing to soften the US stance towards potential future talks, he said: "Let's just meet and let's talk about the weather if you want and talk about whether it's going to be a square table or a round table if that's what you're excited about.
"Then we can begin to lay out a map, a road map, of what we might be willing to work towards."
He also insisted that economic and diplomatic sanctions would continue until "the first bomb drops".
President Trump has repeatedly accused China of not doing enough to rein in North Korea.
Mr Tillerson said that while China was fully implementing sanctions, the president still wanted Beijing to cut off oil supplies to Pyongyang.
He also said China had made contingency plans to accommodate North Korean refugees in the event of a conflict, a major concern for China.
On Wednesday, North Korean state media said leader Kim Jong-un had vowed his country would become "the strongest nuclear power and military power in the world".
Speaking at a munitions industry conference, he cited North Korea's recent launch of intercontinental ballistic missile Hwasong-15 as a "great historic victory".
'Left the door ajar'
The UN's Jeffrey Feltman said that while North Korean officials did not offer any commitments to future talks during his visit, they had agreed that discussions should continue.
"They agreed that it was important to prevent war," he said in his first briefing since his four-day trip last week.
The question of how to avoid war was the topic of more than 15 hours of talks with North Korea's foreign affairs minister Ri Yong Ho and vice-minister Pak Myong Guk, he said.
"We've left the door ajar and I fervently hope the door to a negotiated solution will now be opened wide."
