In a nationally televised press conference, Park Geun-hye said she would “meet with anyone if necessary to open the path of a peaceful unification”.
Kim Jong-un offered talks with South Korea if the conditions were right in his New Year address.
Leaders of South Korea and North Korea have only met twice, in 2000 and 2007, since the Korean War which divided the peninsula.
Kim Jong-un had said on January 1 that “depending on the mood and circumstances”, there would be “no reason” not to hold a high-level summit on the reunification of the two Koreas.
On January 12, Park Geun-hye delivered her own New Year message saying she would set no conditions to the talks, but added that North Korea should take “sincere” steps towards denuclearization.
North Korea has conducted three nuclear tests in recent years, aggravating relations with the South.
It has offered to put a moratorium on testing nuclear weapons if South Korea halts military exercises it holds with American forces. That offer was rejected and the two allies plan to hold a joint naval drill this week, reported South Korean news agency Yonhap.
Park Geun-hye also called on North Korea to “come forward for dialogue without hesitation” on efforts to reunite families separated since the end of 1950-53 Korean War.
The last formal high-level talks were in February 2014, leading to rare reunions for Korean families separated for over 60 years.
However, further talks planned in October were dropped after North Korea accused South Korea of not doing enough to stop activists sending anti-Northern leaflets across the border on balloons.
The two Koreas have technically been at war since the Korean War ended in an armistice rather than a peace treaty.
Park Geun-hye also addressed the use of a controversial law to deport Korean-American Shin Eun-mi on January 10.
South Korea has put in place a National Security Law which states that anyone who praises North Korea can be jailed for up to seven years.
The law was used to deport Shin Eun-mi for speaking positively about life in North Korea in speeches and in online posts. Shin Eun-mi has denied she praised North Korea.
Critics say the controversial law suppresses freedom of speech.
Park Geun-hye defended the law’s use, saying it was needed to “ensure security in this country as we remain in a standoff with the North”.
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