The North Korean statement said US bases in “Japan, Guam and the US mainland” were within its “scope of strike”.
It follows Seoul’s announcement on Sunday that it would almost triple the range of its own missile system.
Pyongyang is thought to be working on a long-range missile, but two recent rocket tests ended in failure.
North Korea’s neighbors said the failed rocket launches – in April 2009 and April 2012 – were tests related to the development of the long-range Taepodong-2 missile system.
The system, which analysts believe is intended to put the US mainland within striking range, has not yet been tested successfully.
North Korea routinely issues strong rhetoric against Seoul and Washington.
But the Communist state does possess an array of short- and medium-range missiles, as well as artillery pointed towards South Korea.
The statement, carried by state-run KCNA news agency and attributed to North Korea’s National Defence Commission, said Pyongyang would match any enemy “nuclear for nuclear, missile for missile”.
It added that the missile deal between the US and South Korea was “another conspiracy of the master and the stooge to push the situation on the Korean Peninsula to the extreme… and ignite a war”.
On Sunday, South Korea announced it had reached an agreement with the US on extending the range of its ballistic missiles.
Under a previous security deal with the US, it had been restricted to missiles with a range of 300 km (186 miles). The new deal extends that range to 800 km.
National Security Adviser Chun Yung-woo said the aim was to curb “military provocations by North Korea”.
The two Koreas remain technically at war following the 1950-53 Korean War, which ended in an armistice.
The US has more than 28,000 troops in South Korea and provides security guarantees for its ally.
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