The warning came after the USA sanctioned three North Korean officials last week, . including Choe Ryong-hae, a top aide to Kim Jong-un.
North Korea has condemned the United States for stepping up sanctions and pressure on the regime.
"Now, the global society is unanimous in welcoming the proactive denuclearization steps taken by the DPRK and urging the U.S.to respond to these steps in a corresponding manner", it reads.
The statement said the top leaders of the DPRK and the United States committed themselves to improving the DPRK-U.S. relations at the historic DPRK-U.S. summit held in Singapore in June, and now the bilateral relations are advancing along the firm will of the two leaders to follow through their joint statement issued then.
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The editorial also said that "added sanctions pressure will block the path to denuclearization on the Korean peninsula forever - a result desired by no one".
The Korean Central News Agency (KCNA) said Kim Jong-un placed floral tributes in front of the statues of his father and his grandfather Kim Il-sung, the founder of the country, and later paid tribute to his father's embalmed body, reports Efe news.
In this photo, taken April 25, 2002, then North Korean leader Kim Jong Il claps from the balcony as soldiers salute him during a military parade, celebrating the foundation of the armed forces in Pyongyang, North Korea.
Former U.K. Ambassador to North Korea John Everard told Voice of America that the North siphons off portions of worldwide aid for use by its military and elite. Moon later said that Kim would visit "within this year".
Despite the latest war of words, a second summit between Mr Trump and Mr Kim is expected to be held next year.
It was his first public activity reported by the country's media in two weeks.