The statement by Kim Yong Chol came just a day after Kim Yo Jong, the powerful sister of leader Kim Jong Un, demanded Washington withdraw its forces from the peninsula.
The US and South Korean militaries began their preliminary training Tuesday in the run-up to next week's yearly summertime exercise, which the nuclear-armed North has long considered a rehearsal for invasion.
Pyongyang will make the Seoul authorities realise "what a serious security crisis they will face", Kim Yong Chol said in a statement released by the official KCNA news agency.
The South had answered the North's "good faith with hostile acts" after "letting go the opportunity for improved inter-Korean relations", he added.
Kim is a senior official in the ruling Workers' Party and acted as leader Kim Jong Un's envoy ahead of a summit in Hanoi in 2019, meeting then-president Donald Trump in Washington.
The summit collapsed over sanctions relief and what the nuclear-armed North would be willing to give up in return, and talks have since been largely at a standstill, while Pyongyang has retreated behind a self-imposed curtain of coronavirus isolation.
Just last month, Seoul and Pyongyang restored cross-border communications that were severed more than a year ago, announcing their leaders had agreed to work on improving ties.
But on Tuesday afternoon, Seoul's defence ministry said the North did not answer the daily calls made between the two countries on their military hotline, just two weeks after the link was reconnected.
That came after Kim Yo Jong -- a key adviser to her brother -- called Seoul authorities "perfidious" for going ahead with the joint exercises, warning the two allies would face greater security threats.
Seoul and Washington are treaty allies, with around 28,500 American troops stationed in South Korea to defend it against its neighbour, which invaded in 1950.
They have already scaled back their annual joint military exercises significantly to facilitate nuclear talks with Pyongyang.
But Kim Yo Jong said: "For peace to settle on the peninsula, it is imperative for the US to withdraw its aggression troops and war hardware deployed in south Korea", adding the North would strengthen its defence and pre-emptive strike capabilities.
Responding to her statement, US State Department spokesman Ned Price stressed that the joint drills were "purely defensive in nature".
"As we have long maintained, the United States harbours no hostile intent towards the DPRK," he said, using the North's official name.
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