Kim Jong Un met Russian leader Vladimir Putin in September
Mr Kim also said three organisations dealing with reunification would shut down, state media KCNA reported.
South Korea's president said it would respond "multiple times stronger" to any provocation from the North.
The two Koreas have been divided since the Korean War ended in 1953.
They did not sign a peace treaty and therefore have remained technically still at war ever since.
In a speech delivered at the Supreme People's Assembly - North Korea's rubber-stamp parliament - Mr Kim said that the constitution should be amended to educate North Koreans that South Korea is a "primary foe and invariable principal enemy".
He also said that if a war breaks out on the Korean peninsula, the country's constitution should reflect the issue of "occupying", "recapturing" and "incorporating" the South into its territory.
Mr Kim - who replaced his father, Kim Jong-il, as North Korean leader in 2011 - said the North "did not want war, but we also have no intention of avoiding it", according to KCNA.
He said he was taking a "new stand" on north-south relations, which included dismantling all organisations tasked with reunification.
Speaking to his cabinet on Tuesday, South Korean President Yoon Suk Yeol said that if the North carried out a provocation, the South "will retaliate multiple times stronger", pointing to the South Korean military's "overwhelming response capabilities".
Dr John Nilsson-Wright, who heads the Japan and Koreas Programme at Cambridge University's Centre for Geopolitics, described Mr Kim's remarks as "unprecedented", and said it was "highly unusual" for a North Korean leader to depart from the policy of unification.
"It's not unusual for relations between the North and South to cool, but this has taken the relationship in a different direction," he told the BBC.
He added that Mr Kim's anti-Western stance can be traced back to the 2019 summit with then-US President Donald Trump in Vietnam, which ended without an agreement.
"This has been an acute disappointment and loss of face for Kim," Dr Nilsson-Wright said.
-- Courtesy of BBC News