Meanwhile, Bedi left for Chennai on Thursday morning to participate in an event. She is likely to go to Delhi from Chennai.
Narayanasamy began his protest on Wednesday, wearing a black shirt and black dhoti. He was protesting against Bedi for not permitting implementation of his government's welfare schemes.
He was joined by his ministerial colleagues and DMK lawmakers.
Narayansamy also accused Bedi of interfering in the day-to-day activities of the government.
He also asserted that Bedi is being encouraged by Prime Minister Narendra Modi to create problems for his government.
"She (Kiran Bedi) has no power at all, she only has to be a post office and sign papers which have been sent by the council of ministers. She has no right to touch cabinet decisions, she is vetoing decisions," he said.
"She is being encouraged by the Prime Minister to create problems for our government," he added.
His protest came after Bedi hit the road two days ago and advised two-wheeler owners to wear helmets.
While Bedi wanted the helmet rule for two-wheeler riders to be implemented at one go, Narayanasamy wanted the implementation in phases.
On her part, Bedi on Wednesday evening wrote to Narayanasamy inviting him for a meeting on February 21.
Bedi, in her letter to Narayanasamy, said: "All matters you had mentioned in the letter need an examination for a considered response. Needless to say, none of the issues are pending at Raj Nivas (as being alleged). Besides, you never said in your letter that unless you get a reply by February 13, you and your colleagues shall come and sit on a dharna outside."
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