Kim met Trump three times for high-profile summits during Trump's first term, before talks collapsed in Hanoi in 2019 over what concessions Pyongyang was prepared to make on its atomic weapons.
The US demand that Kim give up his banned weapons has long been a sticking point between the two countries, with Pyongyang under successive rafts of UN sanctions over its nuclear and missile programmes.
"If the United States discards its delusional obsession with denuclearisation and, based on recognising reality, truly wishes for peaceful coexistence with us, then there is no reason we cannot meet it," Kim said, according to a report Monday by the official Korean Central News Agency.
"I still personally hold fond memories of the current US president, Trump," Kim added, in a wide-ranging speech to the country's Supreme People's Assembly.
Since the failed 2019 summit, North Korea has repeatedly said it will never give up its atomic weapons and declared itself an "irreversible" nuclear state.
Kim reiterated that denuclearisation was not an option.
"The world already knows well what the United States does after it forces a country to give up its nuclear arms and disarm," he said.
"We will never give up our nuclear weapons."
Kim said sanctions had only helped the North in "growing stronger, building endurance and resistance that cannot be crushed by any pressure".
Kim also added he had "no reason to sit down with South Korea", even as Seoul's new President Lee Jae-myung has sought to ease tensions with the North.
"We make it clear that we will not deal with them in any form," he said.
Kim's speech reiterates Pyongyang's position that it must be recognised as a nuclear state before any talks can take place, Hong Min, a senior analyst at the Korea Institute for National Unification, told AFP.
"It reaffirms the North's stance that recognition as a nuclear-armed state, along with a willingness to improve relations with it, are the prerequisites for dialogue," he said.
"It calls for a fundamental shift toward equal dialogue and improved relations as a nuclear-armed state."
North Korea has in recent years declared the South its principal enemy and blown up rail links and roads connecting the two countries.
- Russia ties -
"The lengthy and detailed justifications reflect equal parts confidence and desperation," Yang Moo-jin, former president of the University of North Korean Studies in Seoul, told AFP.
"While outwardly aimed at foreign powers, the speech carried a strong domestic message, seeking to pre-empt instability," Yang said.
Kim has been emboldened by the war in Ukraine, according to analysts, securing critical support from Russia after sending thousands of North Korean troops to fight alongside Moscow.
North Korea has become one of Russia's main allies since Moscow invaded Ukraine three-and-a-half years ago, sending thousands of soldiers and container loads of weapons to help the Kremlin push Ukrainian forces out of western Russia, following Kyiv's shock incursion last year.
Moscow and Pyongyang signed a mutual defence pact last year when Russian President Vladimir Putin visited the reclusive state.
Seoul has repeatedly warned that Russia is stepping up support for Pyongyang, including the potential transfer of sensitive Russian military technology.
Trump is expected to visit South Korea next month, when the country hosts the Asia-Pacific Economic Cooperation Forum (APEC) in its southern city of Gyeongju.
"The timing of the remarks, just ahead of Trump's trip to South Korea for the APEC summit, appears calculated," said Lim Eul-chul at South Korea's Kyungnam University.
"It hinted at the possibility of a surprise summit, while also playing to Trump's well-known yearning for a Nobel Prize."
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