Kerry, in Sydney for joint security talks with his Australian counterpart Julie Bishop, said both sides had discussed hopes for a peaceful move towards a denuclearised Korean peninsula.
"The United States, I want to make this clear, is absolutely prepared to improve relations with North Korea if North Korea will honour its international obligations. It's that simple," he said.
"But make no mistake, we are also prepared to increase pressure, including through strong sanctions and further isolation, if North Korea chooses the path of confrontation."
"If the US imperialists threaten our sovereignty and survival... Our troops will fire our nuclear-armed rockets at the White House and the Pentagon - the sources of all evil," Hwang Pyong-So, director of the military's General Political Bureau, said in a speech.
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Hwang, who holds the rank of vice marshal in the Korean People's Army, said a recent series of South Korea-US military drills, one of which included the deployment of a nuclear-powered US aircraft carrier, had ramped up tensions.
The North often test-fires missiles and rockets into the sea as a show of force or to express anger at perceived provocations, but the frequency of recent tests has been unusual.
UN resolutions bar North Korea from conducting any launches using ballistic missile technology. The North has defended the launches as a legitimate exercise in self-defence and a response to US war manoeuvres.
Already under crippling sanctions since 2006, Pyongyang was hit by fresh UN punitive measures in March 2013 over its third nuclear test.