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US President Donald Trump has said talks with North Korea could take place "over the next three or four weeks".

"It's going [to] be a very important meeting, the denuclearisation of the Korean peninsula," he said.

Meanwhile, new Secretary of State Mike Pompeo said he had had a "good conversation" with North Korea's leader Kim Jong-un in Pyongyang recently.

On Friday, Mr Kim and the South Korean President Moon Jae-in agreed to work to rid the peninsula of nuclear weapons.

The inter-Korean summit at the border came just months after warlike rhetoric from the North.

Mr Kim became the first North Korean leader to set foot in South Korea since the end of the Korean War in 1953.

• Historic summit as it happened
• Five key moments from the meeting
• Read the Korean declaration in full

For years, Pyongyang has insisted that it would never give up its nuclear arsenal, which it claims it needs to defend itself against aggression from the US.

What did President Trump say?

Speaking at a rally in Washington, Michigan, he said: "I think we will have a meeting over the next three or four weeks."

He said he hoped for successful negotiations on the denuclearisation of the Korean peninsula.

But the president added that he was ready to walk away if the talks did not work out.

North Korea has not publicly commented on Mr Trump's latest statements.

Earlier on Saturday, Mr Trump tweeted that "things are going well" and that preparations were being made for his summit with Mr Kim.

Separately, Mr Pompeo told ABC News that Mr Kim was "prepared to... lay out a map that would help us achieve" denuclearisation.

Mr Pompeo described the North Korean leader as "very well prepared" during their talks in Pyongyang.

US officials are still deciding where to hold the talks between President Trump and Mr Kim - but Mongolia and Singapore are understood to be two countries on the shortlist.

What was agreed at the inter-Korean summit?

Mr Kim and Mr Moon said they would pursue talks with the US and China to formally end the Korean War, which ended in 1953 with a truce, not total peace.

The commitment to denuclearisation does not explicitly refer to North Korea halting its nuclear activities but rather to the aim of "a nuclear-free Korean peninsula".