No motive has been confirmed and the attackers have not been identified.
South Korea’s acting President Hwang Kyo-ahn said if North Korea was found to be responsible, it would show its “brutality and inhumane nature”.
It would be the most high-profile death at the hands of the North Korean leadership since Kim Jong-un’s uncle, Chang Song-thaek, was executed in 2013.
Mr Hwang said South Korea was “keeping close tabs on North Korea’s movements”.
North Korea has not commented on the death but officials from the country’s Malaysian embassy have been visiting the hospital in Kuala Lumpur where Mr Kim’s body has been taken.
Mr Kim was attacked while preparing to board a flight home to Macau. His death was only made public on Tuesday.