The North Korean leader, Kim Jong-un, has suggested he would be open to talks with the US, while South Korea’s president has hinted he would accept a deal between Kim and Donald Trump that allowed the North to retain its existing nuclear weapons.

In a speech to the Supreme People’s Assembly on Sunday, Kim said he still had “fond memories” of Trump, whom he met three times during Trump’s first term as US president.

Those talks failed to halt North Korea’s nuclear programme and triggered a breakdown in 2019 of high-level negotiations between Pyongyang and Washington, while Kim has since formed stronger diplomatic and military ties with Russia and China.

But in an apparent sign that the door to dialogue has reopened – if only slightly – Kim said there was “no reason for us not to sit down with the United States”, the state-run KCNA news agency reported on Monday.

But there would be key caveats, Kim added, including Washington dropping “the absurd obsession with denuclearising us and accepts reality, and wants genuine peaceful coexistence”.

Kim’s comments were reported as the South’s new president, Lee Jae Myung said he would accept a deal between Trump and Kim that only required Pyongyang to halt its production of nuclear weapons rather than destroy its entire arsenal.

A freeze on North Korean nuclear weapons as “an interim emergency measure” would be “a feasible, realistic alternative” to complete denuclearisation, Lee, a liberal who favours engagement with his neighbour, told the BBC, adding that the North was producing an additional 15 to 20 nuclear weapons a year.

Lee, who was elected in June after the impeachment and removal from office of Yoon Suk Yeol, added: “So long as we do not give up on the long-term goal of denuclearisation, I believe there are clear benefits to having North Korea stop its nuclear and missile development.”

“The question is whether we persist with fruitless attempts towards the ultimate goal [of denuclearisation] or we set more realistic goals and achieve some of them.”

Despite his conciliatory tone, Kim has made it clear that North Korea has no intention of relinquishing its nuclear weapons – a move he conceded could fatally weaken his regime.

Describing his nuclear programme as a “matter of survival” amid threats from the US and South Korea, Kim said: “The world already knows full well what the United States does after it makes a country give up its nuclear weapons and disarms. We will never give up our nuclear weapons.”

In an interview with Reuters, Lee conceded that decades of UN-led sanctions had failed to prevent the North from expanding and improving its arsenal of weapons of mass destruction.

“The reality is that the previous approach of sanctions and pressure has not solved the problem; it has worsened it,” he said.

Lee has attempted to ease tensions on the Korean peninsula after a dramatic deterioration in cross-border ties under Yoon, a conservative who took a hard line against the Kim regime. Instead, he has called for the resumption of inter-Korean dialogue and a more “realistic” piecemeal approach towards denuclearisation.