"That I would like to support and welcome."
Washington has said it would only be willing to hold talks with North Korea on the sidelines of the six-party dialogue – which involves envoys from China, Japan, Russia, the US and the two Koreas.
US officials believe any other negotiations would marginalise its two closest allies in Asia – Japan and South Korea – and reward the North for its behaviour.
The six-nation disarmament talks hosted by Beijing ground to a halt in December over North Korea's refusal to put into writing any commitments on inspecting its past nuclear activities.
The failure blocked progress on an aid-for-disarmament agreement reached in 2007.
Then in April North Korea announced it was walking away from the six-party talks altogether following a rebuke from the United Nations Security Council over its launch of a long-range rocket.
Since then it has tested a second nuclear device and said on several occasions that it regards the disarmament talks as dead.
North Korea's surprise offer of direct talks with the US came on Monday, shortly after Hillary Clinton, the US secretary of state, had reiterated Washington's position that the six-party structure was the "appropriate way" to engage the North.
Complicating relations between North Korea and the US is the case of two American journalists arrested near North Korea's border with China in March.
The two reporters, Laura Ling and Euna Lee, were sentenced in June to 12 years of hard labour for entering the country illegally and for unspecified "hostile acts".
Commenting on the North Korean talks proposal, the UN secretary general, himself a former South Korean foreign minister, said he would be willing if necessary to travel to Pyongyang to pave the way for fresh dialogue.
"This situation on the Korean peninsula is very serious, and whatever I can do as the secretary-general I am willing to do, including my own visit to Pyongyang," he said.
"At this time, however, I need to find out when would be an appropriate timing for me to visit."