Trump also assured that Kim will remain in power if he agrees to denuclearise the Korean peninsula. 

"They've been negotiating like nothing happened," the US President was quoted as saying by CNN about North Korea.

"If the meeting happens, it happens. And if it doesn't, we go on to the next step," Trump said. "We may have the meeting. We may not have the meeting. If we don't have it, that will be very interesting. ... We'll see what happens."

However, Trump said in case of North Korea the so-called "Libya model" for denuclearisation is not being pursued.

Libyan leader Muammar Gaddafi agreed to give up his nuclear programme  in 2003 but was killed by western-backed rebels later that year.   

The suggestion on the model was given by US national security adviser John Bolton, media reports said.

The suggestion had prompted alarm in North Korea.

He said the deal his government has been thinking about Kim Jong-un would be "something where he'd be there, he'd be in his country, he'd be running his country, his country would be very rich."

Meanwhile, earlier this week, North Korea had threatened to cancel the upcoming talk between Trump and Kim if the former unilaterally insists the latter gives up nuclear weapons, media reports said on Wednesday.

Kim and Trump are scheduled to meet in Singapore on June 12.

Improvement in relationship between the South and the North in recent times

Relationship between South and North Korea seemed to have improved in recent times with Kim Jong-un meeting South Korean President Moon Jae-in at the Panmunjom peace village on Apr 27.

The neighbouring leaders shaking hands over the Military Demarcation Line grabbed attention all over the world.

US, Trump and North Korea

2017 witnessed US President Donald Trump slamming North Korean leader Kim Jong-un as the Asian nation continued to conduct several of its missile tests, teasing world peace and tranquillity and often threatening to trigger a war.

Situation became far tensed when North Korea tested an inter-continental ballistic missile (ICBM) that it said was capable of striking US mainland.

The United Nations Security Council imposed strong new sanctions against the Asian nation after its Nov 29 launch of a nuclear-capable weapon.

Trump and North Korea continued to exchange barbs earlier this year too.

Fresh development in the relationship between North Korea, South Korea and the US began recently when a North Korean delegation was invited to the Winter Olympics in Pyeongchang.

Trump and Kim agreed to meet on June 12, signalling improved relationship between the two nations.

Three United States nationals were also released by North Korea this month.

The move was appreciated by the United Nations.