US President Donald Trump has agreed to meet with North Korean leader Kim Jong Un, the White House announced, as quoted by CNN.

CNN reported that the meeting, which would be the first between a sitting US president and a North Korean leader, will take place by May, according to South Korea's national security adviser, Chung Eui-yong, who delivered the invitation to Trump after a visit by his delegation to Pyongyang earlier this week.

The South Korean delegation was careful to praise Trump's influence over the developments. Chung said the US President's "leadership" and his administration's pressure on the North Korean regime had "brought us to this juncture", the report said.

White House press secretary Sarah Sanders said in a statement that Trump "greatly appreciates the nice words" of the delegation and South Korean President Moon Jae-in.

"He will accept the invitation to meet with Kim Jong Un at a place and time to be determined. We look forward to the denuclearization of North Korea. In the meantime, all sanctions and maximum pressure must remain," the statement added.

Trump tweeted that "great progress" had been made but there would be no prospect of lifting sanctions until a deal was reached.

South Korea's President Moon described the announcement as "historic" and and thanked both leaders for seeking a diplomatic solution to the denuclearization of the Korean Peninsula.

"This is an almost miraculous event; my administration will prepare toward the May meeting with utmost diligence," he said in remarks read out in Seoul by a Blue House spokesman.