Kang and the South Korean delegation were in the United States to pay their respects to former President George H.W. Bush at the U.S. Capitol. They attended the funeral on Wednesday.
The two diplomats are meeting for the first time since Oct. 7, when Pompeo visited Seoul following his fourth trip to North Korea.
The meeting began at 8:30 a.m. at the State Department. Sources told Yonhap the meeting covered cooperation on North Korea denuclearization, and other areas where the two countries need to coordinate policy.
Foreign ministry spokesman Noh Kyu-duk had said ahead of the meeting the denuclearization of the Korean Peninsula and the establishment of the peace process are to be discussed to "maintain coordination," as confirmed by the "Nov. 30 summit meeting."
Talks come a day after South Korean railroad surveyors returned from inspecting train tracks in the North.
South Korean television network JTBC reported Thursday the tracks were mostly single-track and worn out.
The condition of the train tracks made it difficult to raise the speed of cars, experts said.
Other areas of the railroad, including the tracks that connect China to North Korea, were well maintained, they added.
One expert who had visited the North said the North's side of the Gyeongui Line was in better shape than in 2007.