“Let’s just meet and let’s talk about the weather if you want,” he said at a policy forum in Washington DC.
His statement appeared to shift the US position away from previous demands that North Korea must first disarm.
North Korea’s pursuit of nuclear weapons technology has led to heavy US-led sanctions against the regime.
Elsewhere in his remarks, Mr Tillerson insisted that the economic and diplomatic sanctions would continue until “the first bomb drops”.
Diplomatic relations between the two nations have been strained by recent North Korean 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, Mr Tillerson said that the US “simply cannot accept a nuclear armed North Korea”.
But appearing to soften the US stance to 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.”
Mr Tillerson also said that China had made contingency plans to accommodate North Korean refugees in the event of a conflict. (Courtesy BBC)