The previous day, Trump warned the United States would hit the North with "fire and fury" if Pyongyang repeated threats that it would strike American targets, Trump took to Twitter and appeared to signal he is prepared to use nuclear weapons against North Korea if conflict breaks out.
However, the North and South resumed dialogue in January after a two-year gap in order to discuss joint participation in the Winter Olympics.
Chung Eui-yong, head of the presidential National Security Office, Suh Hoon, chief of the South's National Intelligence Service, and other members of South Korean delegation pose before boarding an aircraft as they leave for Pyongyang at a military airport in Seongnam, south of Seoul, South Korea March 5, 2018.
The delegation will be led by security officials as part of an effort to lower tensions on the Korean peninsula as well as possibly arrange talks between North Korea and the United States, it said.
On the other hand, a number of analysts question whether North Korea would want to respond by attacking the South even if the United States staged a strike.
The North's official Korean Central News Agency also announced their impending visit in a one-paragraph dispatch.
Trump, however, has stated that the US and North Korea can meet only "under the right conditions".
Moon had previously called on his neighbor to speak with the USA before a possible third inter-Korean summit - the last of which took place more than a decade ago. "We will be meeting, and we will see if anything positive happens".
Mr Chung had earlier told a press briefing he would deliver President Moon Jae-in's "resolution to maintain the dialogue and improvement in relations between the South and the North".
"War and chaos on the peninsula in not in the interests of any side", Zhang said.
The Games, which ended on February 25, saw the sister of North Korean leader Kim Jong Un make the first visit to the South by a member of the Kim family since the end of the Korean War in 1953.
During a joke-filled monologue at a dinner with journalists in Washington on Saturday (local time), Mr Trump suggested that the United States would be meeting with North Korea but has told Pyongyang it must first "denuke".
A North Korean Ministry of Foreign Affairs spokesperson told the official Korean Central News Agency on Saturday that the country wouldn't accept USA preconditions. He did not specify exactly what conditions would be "right", but certainly he's not interested in negotiations while North Korea continues to engage in insults, to deride him in editorials and, above all, to persist in threatening the United States with nuclear attack.
In the past, South Korea sent special envoys to Pyongyang to reach breakthrough deals aimed at reducing animosities and securing higher-level talks.
Last year, the isolated and impoverished North staged its most powerful nuclear test and test-fired several missiles in defiance of United Nations sanctions. To some extent, one can say that even Russian Federation and China share this concern of nuclear proliferation in general and in the Korean peninsula, because for example, if Iran develops nuclear weapons then Saudi Arabia will do so, and other Gulf states will be tempted to do so.
The White House said the leaders "noted their firm position that any dialogue with North Korea must be conducted with the explicit and unwavering goal of complete, verifiable and irreversible denuclearisation".