Park made her comment in a Liberation Day address marking the end of Japan's 1910-45 rule of the Korean Peninsula, Yonhap News Agency reported.
The Koreas have held 18 reunions since agreeing to the process in 2000.
Yonhap reported that more than 20,000 family members separated since the 1950-53 conflict were reunited before the last reunion in 2010.
Some of the last visits in 2010 were three-day events organized with the help of the International Red Cross which provided the facilities, including tents and food for families.
More than 430 South Koreans, from 97 families and aged 12 to 60 years, were bused across the demilitarized zone -- the border -- to North Korea's resort of Mount Kumgang on the coast of the Sea of Japan.
Park's suggestion to resume the reunions comes a day after North and South Korea agreed to reopen a joint factory complex in the North Korean border city of Kaesong.
"I hope the [Kaesong] agreement this time will serve as an opportunity to remedy what went wrong in inter-Korean relations in the past and help build a new relationship of mutual prosperity," Park said in her address.
"First and foremost, we have to ease the pains of separated families," Park said. "I hope the North will be able to work together to make the reunion of the separated families possible around the time of the upcoming Chuseok holidays [Sept. 19].
"In addition, I propose to the North the creation of an international peace park at the Demilitarized Zone, which is a legacy of division and confrontation between the two Koreas."
North and south Korean forces signed a cease-fire agreement in 1953, which created the two countries that remain technically at war. The cease-fire divided the Korean peninsula along the 38th parallel that has acted as the nearly 155-mile border and created the two countries.
North Korea, to ease its employment problems, agreed with the South to set up the Kaesong industrial complex in Kaesong, North Korea's third-largest city, in 2005.
The original agreement allowed more than 120 South Korean textile and other labor-intensive factories to be set up that eventually employed more than 53,000 low-cost North Korean labor.
Around 900 South Koreans worked in the complex that made around $470 million of goods in 2012, the New York Times reported in March.
But North Korea closed down the complex amid rising tensions with the South that led North Korea's communist government to threaten nuclear strikes against Washington and Seoul, the New York Times report said.
Despite the agreement to open the complex, no date has been set, the BBC reported.
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