"Secretary Pompeo and Foreign Minister Kang agreed that pressure must continue until the DPRK denuclearizes," the release said. The two leaders also reaffirmed the strength of the US-South Korea alliance during their phone conversation on June 28, the document noted.
The diplomats also discussed the next steps on engaging with North Korea after the summit in Singapore between US President Donald Trump and North Korean Leader Kim Jong Un.
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Pompeo is scheduled to visit North Korea next week, according to US media reports.
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Meanwhile, the issue of North Korea's denuclearization has been also on the agenda of US Defense Secretary James Mattis' talks with Japanese Prime Minister Shinzo Abe, which met in Tokyo on Friday. Mattis arrived in Tokyo at the end of his five-day trip to the Indo-Pacific region. Earlier this week, Mattis visited Beijing and Seoul.
"The sides exchanged views on the situation in North Korea, confirmed the desire of North Korean leader Kim Jong Un for complete denuclearization of the Korean Peninsula during the US-North Korea summit, and agreed that the summit was a step toward a comprehensive solution to complex issues," the statement, obtained by Sputnik, read.
READ MORE: US, S Korea Say UN Sanctions on Pyongyang to Be Kept Until Full Denuclearization
According to the statement, Mattis stressed that both Japan and the United States supported the compliance with the UN resolutions as well as the demand for concrete actions on the part of North Korea to implement the full and irreversible destruction of weapons of mass destruction and ballistic missiles of all ranges.
On June 12, US President Donald Trump and Kim met in Singapore where they issued an agreement that required Pyongyang to denuclearize in exchange for a freeze on the US-South Korean military drills and eventual sanctions relief. The North Korean leader confirmed his desire to denuclearize and signed a corresponding agreement with South Korean President Moon Jae-in at the inter-Korean summit in late April.