North Korean leader Kim Jong-un committed to "work toward" complete denuclearization of the Korean Peninsula when he met with Trump in Singapore in June.
Woo said the blunt statement on state media can be seen as heightened provocation from Pyongyang seeking to raise the stakes for potential second summit between Trump and Kim.
"The United States must now recognize the accurate meaning of the denuclearization of the Korean Peninsula, and especially, must study geography the right way", the statement said.
Morgulov's statement offered a different view from US policymakers who have credited the Trump administration's policy of "maximum pressure", including heavy sanctions, for bringing North Korea to the negotiating table.
"When we talk about the Korean Peninsula, it includes the territory of our republic and also the entire region of [South Korea] where the United States has placed its invasive force, including nuclear weapons".
Biegun said the United States came to have "greater confidence about the safety and security of Americans travelling to the DPRK" after North Korea in November released an American held for an alleged illegal entrance to the country.More news: Apple to stop potential iPhone ban in China with a software update
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The Trump administration's special envoy for North Korea is heading to South Korea amid stalled progress in denuclearization efforts.
The Prime Minister also shared four photographs of his meeting with the South Korean delegation.
"When we refer to the "denuclearization of the Korean Peninsula" as well, it should be correctly understood as removing all nuclear threat factors from not only the North and the South but from all neighboring areas". Washington wants these to be inspected and dismantled before it will lift sanctions on Pyongyang, but North Korea insists that sanctions must be lifted first. Confirmation of the location, size and use of each site is a key USA demand in the ongoing talks. -South Korea alliance as Trump pursues another summit with Kim, which the president said could come as soon as next month. Several reports from private analysts in recent weeks have accused North Korea of continuing nuclear and missile development, citing details from commercial satellite imagery.
The criticism added new tension to a South Korea visit by the U.S.'s North Korea envoy, Stephen Biegun. "So if we lay down our nukes first, that is not denuclearization, but putting us at a state of being defenseless".
"It is obvious that denuclearization of the Korean Peninsula is a joint business that can not be achieved unless both Korea and the United States strive together", the KCNA commentary said.
The two Koreas plan to hold the ceremony at Panmun Station in the North's border town of Kaesong on December 26, amid concerns that the project could undermine global sanctions imposed on the communist state.