The release from state media outlet KCNA cited the head of North Korea's department of US affairs, but did not name the official.
"The discussion of denuclearization may be possible when threats and hurdles endangering our system security and obstructing our development are clearly removed beyond all doubt," the statement read.
New negotiations with the US could happen "in a few weeks," according to the statement.
North Korea's deputy foreign minister Choe Son Hui said previously the talks were likely to happen in late September.
In South Korea, demands for security guarantees from Pyongyang's leadership are seen as an attempt to strengthen its negotiating position.
Pyongyang is also pushing for sanctions against it to be relaxed.
US President Donald Trump and North Korea's leader Kim Jong Un have met three times for talks, but have failed to make any concrete agreements on North Korea's denuclearization.
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