Kim Jong-un has vowed to achieve North Korea's nuclear goals.
The state-owned KCNA news quoted Kim as saying his aim was to establish "equilibrium" in military power with the US.
Kim's statement comes just days after the North launched a ballistic missile over Japan and weeks after it conducted its sixth and most powerful nuclear test.
Meanwhile, world powers are divided on how to respond.
On September 3, North Korea said it had successfully tested a missile-ready hydrogen bomb which is several times more powerful than an atomic bomb.
The development came hours after an earth tremor was detected by seismologists which was 9.8 times more powerful than the one recorded during the North's fifth nuclear test.
The test was met with international condemnation.
On September 15, North Korea fired a ballistic missile which flew over Japan's northern Hokkaido island before landing far out into the Pacific Ocean.
The launch, the second such test in weeks, happened after the North threatened to "sink Japan and turn America to ashes."
Japanese PM Shinzo Abe said Tokyo would "never tolerate" North Korea's dangerous actions.
The US also condemned the launch.
"We should clearly show the big power chauvinists how our state attain (sic) the goal of completing its nuclear force despite their limitless sanctions and blockade," Kim said.
He said North Korea's goal was "to establish the equilibrium of real force with the US and make the US rulers dare not talk about military option for the DPRK (North Korea's full name)."
The UN Security Council unanimously condemned the "highly provocative" North Korean missile launch.
US President Donald Trump said Pyongyang had "once again shown its utter contempt for its neighbors, and the entire world community."
Trump expressed confidence that the US was ready to exercise a military option if needed.
The US earlier said the military option was available but isn't Trump's preferred choice.
Russia has responded by urging caution and has called for "meaningful negotiations" in the wake of America's "regrettably, aggressive rhetoric."
China has accused the US of shirking its responsibility.
China's ambassador to the US, Cui Tiankai said America should do more to ensure "real effective international co-operation on this issue."
"They should refrain from issuing more threats" and focus on resuming dialogue, he said.
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