North Korea and the US held working-level talks at the inter-Korean border village of Panmunjom ahead of US Secretary of State Mike Pompeo's visit to Pyongyang later this week.
Choe and Kim were estimated to have discussed various issues between the US and North Korea, including Pompeo's visit on Friday.
The two officials earlier met before the meeting between North Korean leader leader Kim Jong-un and US President Donald Trump in Singapore on June 12.
During Sunday's talks, Pompeo's letter was reportedly delivered to Kim Yong Chol, vice chairman of the Workers' Party of Korea Central Committee and director of the United Front Department of North Korea.
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