The conditions for dialogue were outlined in a statement from North Korea’s National Defence Commission and carried on official news agency KCNA.
The UN imposed sanctions on North Korea after the country conducted its third nuclear test on February 12.
The US and South Korea’s annual joint military drills began in March.
“If the US and the South enemies… genuinely want dialogue and negotiation, they should take these steps,” the defence commission said.
“The first step will be withdrawing the UN Security Council resolutions cooked up on ridiculous grounds,” the North Korea statement said.
“Second, you need to tell the whole world that you will not get involved in any rehearsal for a nuclear war that threatens our nation. Dialogues and war games can never go together,” it added.
Tensions have been high on the Korean peninsula since North Korea conducted its third underground nuclear test, which resulted in sanctions from the UN.
In recent weeks, the North has threatened to attack South Korea, Japan and US bases in the region.
South Korean President Park Gyeun-hye has made conditional offers of talks with the North, but the North has said that it was merely a “crafty trick”.
The US had also said it was willing to hold talks with North Korea, but only if previous agreements on disarmament were upheld.
Meanwhile, UN Secretary-General Ban Ki-moon urged North Korea to “seriously ” consider a dialogue with the South about Kaesong Industrial Complex.
“I firmly believe that the recent offer of dialogue by the Republic of Korea is genuine and hope that the DPRK takes it seriously,” Ban Ki-moon said on Wednesday.
Kaesong, located inside North Korea just across the demilitarized zone from South Korea, was largely financed by the South to increase co-operation.
North Korea has blocked access to Kaesong since April 3 amid rising tension on the Korean peninsula.
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