Kim Yo Jong also defended North Korea's latest intercontinental ballistic missile (ICBM) launch as an act of self-defence.
The nuclear-armed state on Wednesday test-fired a solid-fuel missile that flew 1,001 kilometres (622 miles) at a maximum altitude of 6,648 km, before splashing into the East Sea, also known as the Sea of Japan.
Its trajectory suggested it was capable of reaching the mainland United States, analysts said.
"Now that the US does not respond to the abandonment of its hostile policy... the DPRK will further put spurs to building up the most overwhelming nuclear deterrence," Kim Yo Jong said in a statement carried by the Korean Central News Agency.
DPRK refers to the North's official name, the Democratic People's Republic of Korea.
The launch was Pyongyang's exercise of "self-defence to defend the Korean peninsula and the Asia-Pacific region from the disaster of a nuclear war", she said, adding that no one could blame the North in the face of Washington's "hostile policy".
She went on to rail against the United Nations Security Council for its response to the launch.
In a joint statement, 10 of the Security Council's 15 members including South Korea condemned the latest test and noted that the North's 20 launches of ballistic missiles in 2023 were "all blatant violations of multiple Security Council resolutions".
Kim Yo Jong slammed the statement, saying it was "unfair and prejudiced".
Earlier this week she accused US military surveillance jets of breaching North Korean airspace, warning that they could be shot down.
In response to the North's string of missile launches this year, Seoul and Washington have ramped up security cooperation, vowing that Pyongyang would face a nuclear response were it to ever use its nuclear weapons against the allies.
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