The US is "ready to talk any time" with North Korea without preconditions, says Secretary of State Rex Tillerson.
But hours later the White House said President Donald Trump's views on North Korea "had not changed".
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".
China and Russia both welcomed Mr Tillerson's comments. The Chinese foreign ministry hoped there would now be "meaningful steps towards dialogue and contact" between the US and the North.
Russian President Vladimir Putin's spokesman said: "Such constructive statements impress us far more than the confrontational rhetoric that we have heard up to now."
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 Mr 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".
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."