A BJP Zilla Panchayat member was hacked to death by a group of men at a gym in Dharwad on Wednesday.
The deceased has been identified as Yogeesh Goudar, a member of Hebballi constituency, police said.
He sustained injuries on the head and neck after being attacked with lethal weapons, they said, adding that a special team has been formed to probe the case.
Former chief minister Jagadish Shettar demanded an "impartial" probe into the incident. He also expressed "doubts" about a political conspiracy behind the murder.
Speaking to reporters in Bengaluru, Home Minister G Parameshwara said, "Investigation is on in this murder. I have directed officials to nab the culprits as soon as possible. One suspicion is that there was a land dispute he was involved in."
Dharwad District in-charge Minister Vinay Kulkarni said the Chief Minister was aware of the incident.
"Investigation is going on and action will be taken against those involved," he said.
Asked about a tiff some Congress leaders had with him during the local body elections recently, he said, "During elections, blame game is common from both sides, but that should not be counted as enmity."
His brother was also murdered by a group of men few years ago.