The Chinese sports delegation, including male and female players, arrived in Pyongyang on Monday afternoon before North Korea's Party Foundation Day on Wednesday, marking the 1945 foundation of the precursor of the ruling Workers' Party of Korea.
And while Trump huffs and puffs, Kang's moves may win approval elsewhere.
While Washington holds a veto on the UN Security Council - meaning it can prevent motions to alter worldwide sanctions - it has no power over Seoul's policies, which include a range of bilateral sanctions against North Korea. Kang's ministry later tried to downplay her comments, saying in a statement that no decision was imminent. "It's an important executive order". Still, the lifting of the 2010 sanctions could offer at least some tangible benefits to the North.
The South Korean foreign ministry also officially denied that the government was reviewing the matter.
The sanctions were emplaced in 2010, following the sinking of a South Korean corvette in the Yellow Sea, in what the South insists was a Northern torpedo attack.
South Koreans are deeply divided along ideological lines and many people still harbor deep anger over North Korea's 1950 attack that started the Korean War. "While there is still a long way to go and much work to do, we can now see a path to where we'll achieve the ultimate goal which is the full and final verified denuclearization of North Korea", Pompeo told reporters at the White House.
Lifting the South's sanctions would have little effect since USA -led global sanctions remain.
Moreover, in prior comments, Kang had also raised the possibility of exemptions from global sanctions.
Kim Jong-un has invited the Pope to visit North Korea in what appears to be a conciliatory gesture to the outside world.
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A tentative meeting has also been penciled in for November if there is still work to be done. Mr Juncker said "I think we need to refrain from this scenario of a no-deal".
South Korea is supplying water in the North Korean border town of Kaesong using a facility in a now-shuttered factory park that had been jointly operated by the rivals.
"Yao is a star among North Koreans", Lu Chao, a research fellow at the Liaoning Academy of Social Sciences, told the newspaper - later adding that the Chinese player would probably have a bigger impact than Rodman in North Korea.
Considerable exemptions would nearly certainly be necessary if the North and South are to carry out their flagship cross-border project: The re-linking of their rail nets.
The two Koreas have held three summits this year. South Korean President Moon Jae-in has been eager to improve diplomatic relations with North Korea.
"On their soil also", Trump added.
"Kang flubs it", the conservative Joongang Daily editorialized.
But it seems unlikely that Kang flubbed it, one expert said.
Kang's comments are likely to increase speculation that Washington was not fully on board before Seoul signed the agreement.
Moon has mostly stayed firm on sanctions despite actively engaging with North Korea and floating the possibility of huge investments and joint economic projects in return for the North's relinquishment of its nuclear weapons.
Kang did not specify what Pompeo was unhappy about.