The United States and South Korea vowed this week that North Korea would face a nuclear response and the "end" of the leadership there should it use its own nukes against the allies, as the two countries' presidents met in Washington.
In Pyongyang's first response to the Washington summit, Kim Yo Jong said the North remained convinced that its nuclear deterrent "should be brought to further perfection."
"The more the enemies are dead set on staging nuclear war exercises, and the more nuclear assets they deploy in the vicinity of the Korean peninsula, the stronger the exercise of our right to self-defence will become," she said, according to the official Korean Central News Agency.
South Korean President Yoon Suk Yeol and US counterpart Joe Biden on Wednesday issued what was called the Washington Declaration, bolstering the US nuclear umbrella over South Korea, which is increasingly nervous about Pyongyang's aggression.
It will involve the "regular deployment of strategic assets" including the first South Korean port visit by a nuclear ballistic submarine in decades, a US official told AFP.
The agreement, however, would "only result in making peace and security of Northeast Asia and the world be exposed to more serious danger, and it is an act that can thus never be welcome", Kim Yo Jong said.
North Korea has defied years of punishing sanctions to continue work on its banned nuclear and missile programmes, and last year declared itself an "irreversible" nuclear power, effectively ending the possibility of denuclearisation talks.
Pyongyang has conducted a record-breaking string of sanctions-defying launches in 2023, including test-firing the country's first solid-fuel ballistic missile -- a key technical breakthrough for Kim Jong Un's military.
Washington and Seoul have ramped up defence cooperation in response, staging joint military exercises with advanced stealth jets and high-profile US strategic assets.
Biden's criticism of the North is "nonsensical...from the person in his dotage," Kim Yo Jong said, employing language similar to that used to attack former president Donald Trump.
In a further swipe at the 80-year-old Biden's age, Kim's sister said Saturday that he was "not at all capable of taking the responsibility... an old man with no future".
She added it was "too much for him to serve out the two-year remainder of his office term", before then calling South Korean President Yoon a "fool".
Seoul condemned Kim Yo Jong's "far-fetched" statement.
It "reflects its nervousness and frustration at the drastically strengthened nuclear deterrence of the Korea-US alliance," South Korea's Unification Ministry said.
The ministry, which is in charge of inter-Korean relations, added that the statement's "rude language" demonstrated "the North's lowly level".
Kim's statement indicates military tensions around the Korean peninsula could "dramatically escalate to a level similar from 2017", Cheong Seong-chang of the Center for North Korea Studies at the Sejong Institute told AFP.
The statement also represents Pyongyang's "strong protest at Biden's remark that the North would face the end of the regime if it carried out a nuclear attack", he said.