North and South Korea remain technically at war because the 1950-1953 Korean War ended in an armistice rather than a peace treaty.
South Korea's military conducted "corresponding" live firing drills on Friday in response to the shelling.
Lee, who narrowly lost the 2022 presidential election, was conscious and being flown to Seoul National University in the capital.
After massive Japan earthquake and tsunami, surrounding countries are hit and issue tsunami warnings.
"If the enemy opt for military confrontation ... our army should deal a deadly blow to annihilate them thoroughly," KCNA news agency quoted Kim as saying.
North Korea vowed to launch three new spy satellites, build military drones, and boost its nuclear arsenal in 2024 as leader Kim Jong Un said US policy is making war inevitable.
The actor had said he was tricked into taking drugs by a bar hostess trying to blackmail him.
Korea has been coming into its own in recent years as an international entertainment powerhouse.
"The US side reiterated that any nuclear attack by the DPRK against the ROK will be met with a swift, overwhelming, and decisive response," a joint US-South Korean statement said on Saturday.
The legacy of Japan's 1910-45 colonial rule of the Korean peninsula remains politically sensitive for both sides.
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