The Pentagon has said North Korean officials have indicated in the past they have the remains of as many as 200 USA troops.
Washington regards the repatriation of the remains as a test of Pyongyang's willingness to implement the agreement the two leaders reached in the June 12 encounter in Singapore, the first-ever summit between the two countries.
Pompeo initially said the two sides had agreed to hold talks on USA remains on Thursday but no North Korea representatives showed up on the border.
Meanwhile, the USA military has brought to Seoul the remains of a South Korean soldier found in North Korea in 2001 during a joint search between the United States and North Korea.
The White House has hailed the summit between Kim and Trump in Singapore as a major breakthrough toward disarming the isolated, nuclear-armed North in exchange for easing of sanctions and other help with economic development. North Korea then proposed meeting U.S. military officials on Sunday, U.S. and South Korean officials have said.
According to sources cited by South Korean news agency Yonhap, Maj. Earlier, three U.S. Forces Korea vehicles arrived at the Tongil Bridge near the border around 8:20 a.m. before putting United Nations flags on them and heading to Panmunjom.
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Pyongyang later proposed a military generals' meeting with the USA -led U.N. Command on Sunday, and Washington accepted it.
The two Koreas will form joint teams for the tournament, which will be held from Tuesday to Sunday in Daejeon, south of Seoul.
Table tennis players of the Democratic People's Republic of Korea (DPRK) arrived here on Sunday to compete in an worldwide table tennis event hosted by South Korea, local TV footage showed. In 2013, the North severed its hotline with the UNC, declaring the armistice that ended the Korean War null and void.
US forces brought some 100 wooden coffins into the DMZ last month, which will be used to transport the remains, according to Yonhap.
Sunday's talks were expected to focus on such details as when and how the remains should be transferred.
He later said he had made progress on setting a timeline for North Korea's denuclearisation.