North Korea has demanded the removal of UN sanctions imposed for its nuclear and missile tests in order to open up any dialogue with the US.
Pyongyang also said Washington must pledge not to engage in "nuclear war practice" with South Korea for it to extend lines of communication.
The North's National Defence Commission's statement, reported by the official KCNA news agency, said:
If the United States and the puppet South have the slightest desire to avoid the sledge-hammer blow of our army and the people ... and truly wish dialogue and negotiations, they must make the resolute decision.
Firstly, the sanctions resolutions by the UN Security Council that were fabricated with unjust reasons must be withdrawn.
President Barack Obama will meet with South Korean President Park Geun-hye on May 7 at the White House to discuss economic and security issues, including "countering the North Korean threat," the White House said.
– White House statement.
President Obama and President Park will also discuss a broad range of economic and security issues, including continued cooperation on denuclearisation of the Korean peninsula and countering the North Korean threat.
US Secretary of State John Kerry said that the stakes are too high for any "long festering territorial disputes" between North and South Korea not to be set aside.
Mr Kerry was speaking in Japan earlier:
The US Secretary of State John Kerry said that North Korea's "dangerous nuclear missile programme" threatens North Korea's neighbours as well as the country's own people.
– The US Secretary of State John Kerry
The North's dangerous nuclear missile programme threatens not only North Korea's neighbours, but it threatens its own people.
The world does not need more potential for war. And so we will stand together and we welcome China's strong statement of its commitment two days ago to the denuclearisation of the Korean Peninsula.
Moving forward together means it is time also to put long festering territorial disputes behind us. The stakes are far too high, and the global economy is far too fragile, for anyone to allow these inherited problems to divide the region; to inflame it.
US Secretary of State John Kerry vowed today to protect his Asian allies a day before a large-scale military rally was expected to be held in North Korea.
There are fears that tomorrow's celebrations to mark the birthday of the nation's founder, Kim Il Sung, could provide an excuse for another missile test.
ITV News' China Correspondent Angus Walker reports from Seoul:
The US Secretary of State John Kerry said today that Washington would defend its Asian allies from North Korea if necessary, but stressed that negotiation of a peaceful solution was preferable.
At a joint news conference with Japan's Foreign Minister Fumio Kishida in Tokyo, Kerry said:
"I think it is really unfortunate that there has been so much focus and attention in the media and elsewhere on the subject of war, when what we really ought to be talking about is the possibility of peace. And I think there are those possibilities."
However, Kerry confirmed that the US would "do what was necessary" to defend Japan and South Korea.
His comments came as North Korea branded South's Korea's calls for negotiation last week a "cunning trick" via the country's KCNA news agency.
US Secretary of State John Kerry has arrived in Japan, the last stop on an Asian tour aimed at reining North Korea's nuclear ambitions.
US Secretary of State John Kerry was en route to Japan, the last stop on an Asian tour aimed at reining North Korea's nuclear ambitions.
Kerry met China's top leaders on Saturday in a bid to persuade them to push reclusive North Korea, whose sole main ally is Beijing, to return to nuclear talks after weeks of threats of nuclear attacks on the United States and South Korea.
Also likely to be high on the agenda in talks in Tokyo are Japan's territorial disputes with China and the future of US bases in Japan.
The US and Japan this month announced an agreement for the return to Japan of a US air base, taking a step to resolving an issue that trouble relations.
US Secretary of State John Kerry said there has been enough confrontational language on North Korea and that he does not want to get into a cycle of threats and counter-threats with Pyongyang.
Mr Kerry was speaking in Beijing after meeting with senior Chinese leaders.