Pyongyang's news agency KCNA reported Monday that Kim made a personal visit on Sunday to the funeral altar of Kang, about whom little is known.
According to the report, Kang was a delegate to the Supreme People's Assembly. The report did not state the cause of his death.
"On Jan. 22, Comrade Kim Jong Un visited the open casket of the deceased, and expressed his deep condolences," KCNA stated.
The North Korean leader reportedly stroked Kang's face and said, "Comrade Kang Ki Sop had such a thirst for his work, exhibited deep responsibility and proved himself a revolutionary warrior who is infinitely loyal to our party."
Top North Korean officials Hwang Pyong So, Choe Ryong Hae and Ri Myong Su accompanied Kim, according to the report.
Kim also delivered his condolences to the surviving family members, and a wreath from the North Korean leader was placed by the altar, KCNA reported.
Pyongyang's civil aviation administration operates Air Koryo, the national carrier airline.
The sudden deaths of North Korean officials have previously invited speculation of foul play in South Korea.
In 2015, when top North Korean politician Kim Yang Gon was announced dead after an alleged car accident, a South Korean analyst said the crash might have been framed.
Yang Moo-jin, a professor at Seoul's University of North Korean studies, said Kim Yang Gon could have become the object of jealousy among rivals.