"If North Korea launches a provocation, we must respond with stern punishment to clearly show the price North Korea has to pay and our determination to protect our nation," Park said in a televised speech at a ceremony for newly commissioned military officers, AFP reported.
The remarks came after North Korea’s leader Kim Jong-Un ordered the country's nuclear arsenal on standby.
The order announced on Friday came a day after the UN approved its harshest sanctions crafted by the US against the impoverished nation, marking a further escalation of tension on the Korean peninsula.
The official KNCA news agency said under Kim's order, nuclear warheads must be “on standby so as to be fired at any moment.”
Kim said the situation had become very dangerous following the adoption of the sanctions, which came just days ahead of joint military drills by the US and South Korea.
North Korea launched several projectiles into the sea about 150 kilometers (90 miles) off the South Korean coast on Thursday in an apparent response to the new sanctions.
On March 2, the UN Security Council adopted the toughest sanctions to ever be imposed against North Korea in order to penalize Pyongyang for its fourth nuclear test and long-range rocket launch, after weeks of negotiations between the US and China, the latter being an ally of North Korea.
North Korea accuses the US of plotting with its regional allies to topple the government in Pyongyang, stressing that it will not relinquish its nuclear deterrence unless Washington ends its hostile policy toward North Korea. It also wants the US to dissolve its military command in South Korea.