Kim made the remarks at a meeting with former diplomats hosted by the Korean Council on Foreign Relations, hours before he meets with a special envoy sent by Japan's new Prime Minister Shinzo Abe to President-elect Park Geun-hye.
"I would like to emphasize that we should develop a future-oriented relationship with Japan, while protecting our territorial sovereignty and calling for Japan to look squarely at its history," Kim said at the meeting.
"Eventually, relations with Japan will pose a big challenge for Korea this year."
Relations between South Korea and Japan have been strained since outgoing President Lee Myung-bak made a visit to Dokdo last August, the first by a South Korean president, and Japan strongly protested the move and renewed its claim to the East Sea islets.
Dokdo, which lies closer to South Korea in the body of water between the Korean Peninsula and Japan, has long been a thorn in relations between the two countries. South Korea keeps a small police detachment on the islets, effectively controlling them.
Later in the day, Kim met with Abe's envoy, Fukushiro Nukaga, a veteran lawmaker and former finance minister.
In his opening remarks, Kim congratulated the inauguration of Japan's new government and said he is "looking forward to a future-oriented relationship" with the Abe government.
Kim told Nukaga that South Korea "wants to further strengthen bilateral relations with Japan in a wide range of sectors while building a mutual trust," according to a senior ministry official who attended the meeting.
Nukaga also voiced hope that the Abe government seeks a "good start" with South Korea's new government, the official said on the condition of anonymity.
However, in a sign of another potential diplomatic headache, Nukaga expressed "regret" over a ruling by a South Korean court a day earlier that rejected an extradition request by Japan for a Chinese national who served a 10-month prison sentence for an arson attack on the Japanese embassy in Seoul.
The 38-year-old Chinese man, Liu Qiang, 38, returned home on Friday.
"In response, Minister Kim told Nukaga that Japan needs to respect the decision by the Korean judiciary," the official said.
Analysts expected diplomatic tensions between South Korea and Japan over history-related issues to continue after the hawkish Abe, who has a long history of controversial remarks toward South Korea, was inaugurated.