Tension on the Korean peninsula has steadily risen during the last several weeks due to saber-rattling by Pyongyang and North Korean leader Kim Jong-un.
Park's offer came after the North ordered work halted last week at a massive industrial complex in the North Korean city of Kaesong, the last instance of economic cooperation between the two Koreas.
A spokesman for the Kim regime called Park's offer "a cunning ploy to hide the South's policy of confrontation and mislead its responsibility for putting the Kaesong Industrial Complex into a crisis."
Yonhap News Agency said Park made the offer, which was intended to "activate the trust-building process."
U.S. Secretary of State John Kerry said Friday in Seoul the United States supports Park's offer to begin a dialogue.
Kerry cautioned North Korea against launching a missile, saying it would be a "grave mistake."