"Minister Kang said during a meeting with director generals that not only has the case been a diplomatic burden for the government, but also that she was sorry for causing concern to the public," her office said in a press release.
Kang said also that the presidential office had found problems with how the ministry had handled the case.
"We received the probe outcome...that there were problems in the ministry's response from the beginning of the incident to the calls between the leaders. The foreign ministry will review it and promptly take appropriate measures," Kang said.
According to Yonhap News Agency, it was rare for the ministry to disclose what was discussed during the regular meetings between the minister and her director generals.
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Kim was moved to a post as consul-general of the Philippines, but was dismissed and ordered back to Seoul last month.
The agency reported that Kang has vowed in the meeting to strengthen communication with New Zealand in order for this case to be resolved in a fair manner.
She also reportedly stressed that the ministry will apply stricter standards for sexual misconduct cases in the future, regardless of the time of the occurrence.
Kang also ordered the bolstering of related regulations and education.
The Seoul foreign ministry said last week it was considering resuming arbitration to settle the case after recently receiving a request from the complainant.
The Herald has contacted the complainant for further comments.
A New Zealand Ministry of Foreign Affairs and Trade spokeswoman said earlier this month it was making no further comment on the matter.