The threat came a day after Pyongyang condemned the B-52 flights as an "unpardonable provocation" and threatened military action if they continue.
The Pentagon confirmed that B-52s, taking off from Andersen Air Force base in Guam, had flown over South Korea as part of annual joint exercises that Pyongyang insist are a rehearsal for invasion.
"We cannot tolerate the US carrying out nuclear strike drills, setting us as targets, and advertising them as strong warning messages," a spokesman for the North's supreme army command said.
"The US should not forget that the Andersen base... as well as naval bases at Japan's main island and Okinawa, are all within the range of our precision target assets," he said in a statement carried by the Korean Central News Agency.
Military tensions on the Korean peninsula are at their highest level for years, with North Korea -- angered by UN sanctions imposed after its nuclear test last month -- threatening a second Korean War backed by nuclear weapons.
B-52s have taken part in South Korea-US joint exercises before, but the Pentagon said it had publicised their use this time to underline US commitment to defending its South Korean ally.
"If the enemy threatens us with nuclear weapons, we will respond with stronger nuclear attacks," the North's army spokesman warned.
Accusing Washington of orchestrating the sanctions resolution adopted by the UN Security Council earlier this month, North Korea has already threatened to launch "pre-emptive" nuclear strikes on unspecified US targets.
North Korea has missiles that can strike South Korea and Japan but has yet to demonstrate it has the capability to fire long-range missiles that could reach the United States.
Nevertheless, US Defense Secretary Chuck Hagel announced last week that Washington had decided to bolster missile defences along the US west coast so as to "stay ahead of the threat" from the North Korean regime.
In Seoul, analysts largely dismissed the North's threat to US bases in Japan as the latest in a long-series of bellicose, attention-grabbing statements from Pyongyang.
"This is just more bluster," said Baek Seung-Joo, who heads the North Korea Research Team at the Korea Institute for Defence Analyses.
"It really seems aimed at shifting responsibility for the current tensions to the US and South Korea conducting their joint military exercises," Baek said.
The response from Tokyo was measured. A foreign ministry official voiced regret at the North's "provocative action" but stressed that it would not trigger a strategic rethink.
"We have been doing all we can to prepare for contingencies, cooperating closely with our security ally the United States and with South Korea, regardless of the North's comment today," the official said.
In December, North Korea used a long-range rocket to successfully place a satellite in orbit.
Although Pyongyang insisted the launch was a purely scientific mission, most of the international community saw it as a disguised ballistic missile test.
Experts said the December launch marked a step forward for the North's ambitious missile programme, but stressed it was some way from developing a genuine inter-continental ballistic missile (ICBM) with crucial re-entry capability.
There are also doubts -- despite its nuclear test in February -- whether the North has mastered the technology to miniaturise a nuclear warhead to fit on a long-range missile.
In a further sign of the current, heightened tensions, North Korea issued a public air raid warning Thursday, South Korea's Unification Ministry said.
A Defence Ministry spokesman in Seoul said the alert, issued over state radio, appeared to be a drill as part of a series of military exercises the North has been carrying out in recent weeks.
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