Park's comments came a day after Pyongyang said it would have to reconsider its commitment to the reunion event, citing South Korean-US military exercises and "slanderous" articles in the South Korean media.
The two rivals had agreed at rare talks on Wednesday to hold the reunion for several hundred separated relatives from February 20-25.
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"North Korea must not hurt the separated families so deeply again", a press pool report quoted Park as saying before the start of a security meeting with government and military officials.
Park said the reunion would provide momentum for reconciliation on the Korean peninsula, but voiced concern over "instability" in Pyongyang following the recent purge and execution of North Korea leader Kim Jong-Un's uncle and political mentor Jang Song-Thaek.
North Korea has played both hawk and dove since the start of the year, threatening Seoul if it pushes ahead with the US joint exercises, while also proposing a series of potential tension-reducing measures.
"Recently, North Korea has launched an apparent peace offensive but we must keep our guard up all the more," Park said.
"We must maintain a firm defence posture in order to prevent provocative acts by the North and if it provokes us, we have to punish them thoroughly", she added.
Millions of Koreans were separated by the 1950-53 Korean War, and the vast majority have since died without having any communication at all with surviving relatives.
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