North Korea is yet to give a response on attending the summit with US President Donald Trump.
The United States of America’s president, Mr Trump had on Friday accepted North Korea’s invitation to direct talks.
“We have not seen nor received an official response from the North Korean regime regarding the North Korea-US summit,” a spokesman for the South Korean Ministry of Unification said on Monday.
“I feel they’re approaching this matter with caution and they need time to organise their stance.”
South Korean officials said Mr Kim was prepared to give up his nuclear weapons.
Details on the planned talks remain vague, with no agreement yet on the location or agenda.
Analysts are sceptical about what can be achieved through talks given the complexity of the issues involved.