The US maintains it cannot accept North Korea as a nuclear power, despite it conducting five nuclear tests - including two in 2016 - and has pushed harsh international sanctions against the Pyongyang regime.
"If there is anything the Obama administration has done... it has put the security of the US mainland in the greatest danger," said an editorial carried by North Korea's ruling party newspaper Rodong Sinmun.
"It has burdened the new administration with the difficulty of facing the Juche nuclear state," it said, referring to the North Korean ideology usually translated as "self-reliance".
President Barack Obama has made talks with the North conditional on Pyongyang first making some tangible commitment towards denuclearisation, but today's editorial called the goal an "outdated illusion".
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Although Trump has not laid out a clear direction for his policy on North Korea, he has indicated that he would be open to negotiations with its leader Kim Jong-Un in the US to talk him out of his nuclear ambitions.
But in a phone call with South Korean President Park Geun- Hye today, Trump vowed that US commitment on protecting its ally against the North "will not waver".
"We are going to be with you 100 per cent," Trump said, according to a statement from South Korea's Blue House.
"We will be steadfast and strong with respect to working with you to protect against the instability in North Korea," Seoul quoted him as saying.
After Pyongyang carried out its fourth nuclear test in January, the Security Council adopted the toughest sanctions resolution to date, targeting North Korea's trade in minerals and tightening banking restrictions.
Council members are currently debating a fresh resolution after the North's fifth nuclear test in September.