Updated

President Donald Trump's latest tweets on North Korea have received a muted response in South Korea, where media focused more on U.S. Secretary of State Rex Tillerson's acknowledgement that the U.S. is keeping open direct communication channels with the North.

South Korea's largest daily newspaper, Chosun Ilbo, warned Monday that any U.S.-North Korea talks should not recognize the North as a nuclear state, or the South would be forced to seek nuclear arms too.

Tillerson made headlines on Saturday when he said in Beijing that the Trump administration is probing North Korea's willingness to talk.

On Sunday, Trump tweeted that he told Tillerson "he is wasting his time trying to negotiate with Little Rocket Man," referring to North Korean leader Kim Jong Un.