"The army and people of the DPRK will legitimately counter with their powerful nuclear deterrence the largest-ever nuclear war exercises to be staged by the US and the South Korean puppet forces," the statement added.
The US-led United Nations Command said the four-day drill would involve about 20 ships, including the aircraft carrier USS George Washington, and some 200 fixed-wing aircraft.
It said 8,000 service personnel from the two allies were to take part in the show of force.
Seoul's defence ministry has said the drill had been relocated from the sensitive Yellow Sea (West Sea) to the Sea of Japan (East Sea) in deference to Chinese protests.
But future drills will be held in both seas.
Leonid Petrov, a North Korea expert, told Al Jazeera that tension in the Korean peninsula could soon reach its peak.
"What's happening in and around the Korean peninsula is very worrying," Petrov said.
"The Korean War which started 60 years ago never ended and what we see now is the recurrence of tensions which might lead to the continuation of the Korean War."
North Korea on Friday threatened a "physical response" to the drillswhile the United States accused Pyongyang of waging a campaign of provocation.
Washington said it had no interest in getting into a war of words with the North.
"What we need from North Korea is fewer provocative words and more constructive action," P J Crowley, the US state department spokesman, said.
North Korea has called for the resumption of six-party nuclear disarmament talks that it had boycotted since late 2008.
However, tensions are high on the Korean peninsula over the sinking of a South Korean warship in March, which claimed 46 lives.
South Korea and the US have said the North must admit responsibility for the attack on the Cheonan – which a South Korean-led investigation concluded was sunk by a torpedo fired by a North Korean submarine – before talks can resume.