North Korea also rejects the U.N. Security Council's sanctions measures the vessel was allegedly involved in violating.
Biden last month formally declared his candidacy for the Democratic nomination following months of speculation, with opinion polls now placing him firmly in the lead among 25 other candidates.
The back-and-forth comes after Biden, while out on the campaign trail, recently criticized North Korean leader Kim Jong Un.
Stopping short of an ultimatum or direct statement on future bilateral negotiations, Kim said that "everything depends on the United States" and his country will "carefully watch" Washington's next moves. South Korea is also trying to build public and political support for providing wider food aid to North Korea, either directly or through the WFP.More news: What lies ahead for UK after May's resignation
"Yet, he is self-praising himself as being the most popular presidential candidate".
The verbal lashing comes just days after the presidential hopeful suggested during a rally in Philadelphia that US President Donald Trump was "embracing dictators like [Russian President Vladimir] Putin and Kim Jong-un".
He referred to the acronym for the North's official name, the Democratic People's Republic of Korea.
Previously they alleged that Mr Biden had been involved in plagiarism and fell asleep during a speech by Mr Obama in 2011.More news: Footage of Mario Kart Tour gameplay leaks online
"Given Joe Biden's record of standing up for American values and interests, it's no surprise that North Korea would prefer that Donald Trump remain in the White House", a spokesperson for his campaign, Andrew Bates, told the BBC.
South Korea vowed Monday to move quickly on plans to provide $8 million worth of medical and nutritional aid for North Korean children through United Nations agencies while it also considers sending broader food aid to the country, which says it is suffering its worst drought in decades.
North Korea has warned the United States on Tuesday that its "outrageous" seizure of a Pyongyang's cargo ship could generate consequences over the future of North Korea-US relations.
Since 2018, North Korea has been engaged in denuclearization talks with the United States. A second summit between the two, held in Vietnam in February, collapsed without a deal due to large differences over the scope of North Korea's denuclearization and offers of sanctions relief by the U.S.More news: England captain Eoin Morgan suffers small fracture in training
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