External Link Trump tweet: "Spoke to Prime Minister Abe of Japan, who is very enthusiastic about talks with North Korea".
For so long, the United States has sent aircraft carriers and jet fighters in the seas close to the Korean peninsula and stationed some 20,000 American troops in South Korea.
Chung and Suh had originally been scheduled to meet with President Trump on Friday.
A spokesman for South Korea's Ministry of Unification said the North Koreans were probably "approaching this matter with caution", and that they "need time to organise their stance".
Mr Trump said last week that he had accepted an offer to meet with Mr Kim - an agreement that would make him the first sitting USA president to meet face-to-face with a North Korean leader.
On Saturday, Trump said his talks with Kim could end with no agreement or they could be "the greatest deal for the world".
According to Suh, Abe expressed support for denuclearization talks between the North and the United States, emphasizing that Pyongyang should take "concrete" steps toward dismantling its nuclear program.
Meanwhile President Moon claimed "important changes" were happening in East Asian geopolitics.
Nevertheless, there is no word from Pyongyang about when the talks that the regime is said to have proposed will take place.
The Trump administration on Sunday confirmed that there will be no additional conditions imposed on North Korea before a first-ever meeting of the leaders of the two nations.
Some experts are concerned that North Korea could be seeking to delay worldwide action while strengthening its nuclear program.
Even as the world reacts, North Korea has maintained silence, not responding to Trump's announcement last week.
Cheong Seong-chang is an expert on North Korea at the Sejong Institute in South Korea.
South Korean President Moon Jae-in has accepted Kim's offer to meet near their shared border later next month, a meeting in which Kim was expected to suggested resuming cultural exchanges and family reunions.
"I'm very anxious about that happening again and I would hope that this administration understands that", he said.
The U.S. and the South Korea are also discussing how to conduct upcoming military drills in a way that won't provoke Kim, whose regime views the exercises as a rehearsal for war.
"It's been a tough week and you know he likes to be out there in front of his people with them hooting and hollering, and he enjoyed himself". The T-50A is a variant of the T-50 Golden Eagle now serving in the South Korean Air Force and several other militaries around the world.
The U.S. and South Korea hold military manoeuvrs every year.
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