Updated

The Latest on the situation on the Korean Peninsula (all times local):

6 p.m.

The commander of the USS Ronald Reagan aircraft carrier strike group has told reporters in Hong Kong that his ships have an ironclad commitment to defending U.S. allies, including Japan and South Korea.

Rear Admiral Marc Dalton reiterated President Donald Trump's "resolve to use every lever available to us to convince North Korea to alter its dangerous and aggressive behavior."

He was responding to a question about Trump's combative rhetoric. On Sunday, Trump tweeted that his secretary of state was wasting time trying to start a dialogue with North Korea.

Dalton would not confirm South Korean media reports that the Reagan would head to Korean Peninsula waters. Yonhap news agency cited an unnamed South Korean defense official as saying the U.S. carrier plans to conduct exercises with South Korea's navy.

U.S. Secretary of State Rex Tillerson said Saturday that the Trump administration is probing North Korea's willingness to talk, but Trump tweeted on Sunday that he had told Tillerson that he was wasting his time trying to negotiate.

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4 p.m.

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.