Leader Kim Jong Un told visiting South Korean presidential envoy Chung Eui-yong there was "no reason" for Pyongyang to hold on to its nuclear weapons "if military threats towards the North are cleared and the security of its regime is guaranteed".
Kim was willing to discuss denuclearisation with the US and said Pyongyang would stop nuclear and missile tests while talks are under way, Chung told a briefing, and the North and South agreed to hold a summit next month.
"There are positive points in this agreement," the South's conservative Chosun Ilbo daily said in an editorial.
"However, a question mark still hangs over the key issue -- whether the North is genuinely willing to negotiate away its nuclear arsenal," it said.
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It noted the North promised "verifiable, irreversible and complete" denuclearisation in a 2005 agreement, but went ahead with a nuclear test a year later.
It warned Pyongyang might attempt to weaken international sanctions through a rapprochement with the South, while playing for time to further develop its nuclear arsenal.
The pro-business Joongang Ilbo daily said that an inter-Korean summit -- which would be the third of its kind -- would be meaningless unless it led to the North's denuclearisation.
The North had carried out 12 missile and nuclear tests since the South's President Moon Jae-in took office in May last year, it pointed out, saying Pyongyang's overtures were aimed at avoiding sanctions.
"If the North really wants to have peace take root on the Korean peninsula, it should take concrete steps for denuclearisation", Joongang said.
The agreement "paves the way for a complete denuclearisation in the future", Hankyoreh said.
The North's state media made no mention of the offer in its coverage on Wednesday, with the Rodong Sinmun, the mouthpiece of the ruling Workers Party, instead leading on messages of congratulation sent to Kim for the 70th anniversary last month of the founding of the North's military.
In a commentary the paper said that Pyongyang's possession of a nuclear arsenal was justified.
"It was a shining victory for us in our struggle to achieve a parity in power with the US that we have come to develop hydrogen bombs and ICBMs," it said.
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