As people lined up on both sides of the road, the man chanted "Modi, Modi" and came close to the motorcade when the Prime Minister was proceeding to Lalith Mahal Hotel, where he was staying overnight.
The incident happened near V V circle after Modi attended the birth centenary celebrations of Shivarathri Rajendra Mhaswamiji of Sri Suttur Math, according to police.
"A person, who was shouting Modi-Modi, was seen running parallel to the convoy of the Prime Minister. The local police have taken the man into custody and are inquiring," DGP Om Prakash told PTI in Bengaluru.
Asked how serious the incident was as the person was carrying a bag, he said, "The Mysuru police commissioner is scrutinising the footage, and if there is any suspicion on the person's part, action would be taken.
"Asked about the content in the bag, he said "If there is something, local police will get in touch with me. For now, there is no such update from their side."
In the sketchy footage of the incident caught on mobile camera and beamed by some TV channels, it appeared as if the man waiting on the road for the convoy came close to it, even as others stood on the footpaths.
As the word spread about the incident, activists of a group named "Modi Brigade" staged protests demanding action for the alleged security lapse.
Modi is on a two-day visit to Karnataka, as part of which he covered two engagements in Mysuru today. He will inaugurate the Indian Science Congress on Saturday.
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