South Korea and the United States will continue to work closely together to ensure the success of their leaders' separate summits with North Korean leader Kim Jong-un, Seoul's presidential office Cheong Wa Dae said Wednesday on the outcome of recent talks between the countries' top security advisers.

South Korean President Moon Jae-in is set to hold a bilateral summit with Kim on Friday.

Moon's top security adviser Chung Eui-yong and his US counterpart John Bolton agreed to push for a summit between Moon and the US president before Trump holds a separate meeting with the North Korean leader.

The Chung-Bolton meeting was held in Washington on Tuesday (US time), according to Cheong Wa Dae.

"They agreed that President Moon and President Trump will hold a telephone conversation immediately after the South-North Korea summit and share the outcome of the summit," Moon's top press secretary Yoon Young-chan told a press briefing.

"The two have also agreed to push for a meeting between the two presidents before the US-North Korea summit," he added.

Trump has said his meeting with Kim will likely take place in May or early June. (Yonhap)