Kang was on a 12-day trip of emerging Southeast Asian nations that will also take him to Thailand and Myanmar as part of efforts to enhance cooperation in the region.
On the first leg of his trip, Kang held a meeting with Vietnamese President Truong Tan Sang and Vietnamese parliamentary speaker Nguyen Sinh Hung in Hanoi where they agreed to increase efforts to sign a free trade agreement.
During the meeting, Sang invited South Korea's President-elect Park Geun-hye to visit his country in order to build closer relations, the speaker's office said.
South Korea and Vietnam marked the 20th anniversary of forging diplomatic ties last month.
South Korean Assembly Speaker Kang Chang-hee (L) shakse hands with his Vietnamese counterpart Nguyen Sinh Hung (R) during a meeting in Hanoi on Jan. 15, 2012. (Yonhap)