"Our revolutionary forces are combat-ready to sink a USA nuclear powered aircraft carrier with a single strike", the Rodong Sinmun, the newspaper of the North's ruling Workers' Party, said in a commentary.
The issue has gained added urgency as North Korea prepares to celebrate the 85th anniversary of the foundation of its Korean People's Army on Tuesday. In the past, it has marked important anniversaries with tests of its weapons.
Moon would also not go into details on how to respond to North Korea's possible nuclear test.
The man, Tony Kim, had been in North Korea for a month teaching accounting at the Pyongyang University of Science and Technology (PUST), the institution's chancellor, Chan-Mo Park, told Reuters.
North Korea has carried out five nuclear tests and is working to develop nuclear-tipped missiles that could reach the US.
"Our revolutionary forces are combat-ready to sink a USA nuclear-powered aircraft carrier with a single strike", Rodong Sinmun, the newspaper of the North's ruling Workers' Party, said in a commentary.
China is North Korea's sole major ally but has been angered by its nuclear and missile programmes and is frustrated by Pyongyang's belligerence. He has said all options are on the table to halt the North's nuclear program, including a military strike.
The US government has not specified where the carrier strike group is, but US Vice-President Mike Pence said on Saturday it would arrive "within days".
The fresh threat comes in the wake of Trump announcing that he was sending "an armada" to the Korean waters potentially to deal with threats from North Korea.
Abe also said he and Trump agreed that China should play a large role in dealing with it.
"We believe China has a very, very important role to play", said the USA envoy for North Korea policy, Joseph Yun.
Meanwhile, North Korea detained an American on Friday, South Korea's Yonhap news agency reported, bringing the total number of Americans held by the isolated country to three.
Earlier, Japanese Prime Minister Shinzo Abe described his conversation with Trump as a "thorough exchange of views".
"We agreed to strongly demand that North Korea, which is repeating its provocation, show restraint", Abe told reporters. While White House officials, including US President Donald Trump, kept suggesting that the strike force was headed for the Korean Peninsula, it emerged that the flotilla was in fact heading in the opposite direction at the time.
"The reality of today again proves the decision to strengthen nuclear power in quality and quantity under the banner of pursuing economic development and nuclear power was the correct one", the unidentified spokesman said in a statement issued by the North's state media. The launches are considered to be in violation with the UN Security Council resolution. It has also carried out a series of ballistic missile tests in defiance of United Nations sanctions.
"China is firmly supporting the denuclearisation of the area in the name of stability and peace", he said.