Elangovan, meanwhile, left for Delhi by an evening flight from here to apprise party chief Sonia Gandhi over the situation arising out of his alleged remark.
On August 14, he allegedly made derogatory remarks about a meeting between Prime Minister Narendra Modi and Jayalalithaa.
The high court case pertains to a police complaint filed by a former woman worker of a Congress party-run trust against Elangovan, levelling some charges.
The court, however, declined to provide any immediate relief by passing interim order on his anticipatory bail plea.
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Justice S Vaidyanathan, before whom the plea came up, said he does not want to pass any interim order and posted it for further hearing on Monday.
The state is abuzz with the development as technically police is free to arrest Elangovan if it deems it necessary.
Meanwhile, AIADMK held a massive protest demonstration in Tiruchirappalli, condemning Elangovan. Similar protests were held in some other locations in the state as well.
The Tiruchirappalli stir witnessed chaotic scenes and ruckus as a Congress hoarding was brought down by unidentified men and stones were pelted between supporters of ruling AIADMK and Tamil Nadu Congress. Police removed the protesters from the spot and detained them.
In an unprecedented move, BJP Tamil Nadu President Tamilisai Soundararajan in a direct letter to Sonia Gandhi, sought strict action against Elangovan and an unconditional apology from him.
Expressing her party's anguish, she said, "the unparliamentary words used by E V K S Elangovan against Prime Minister Modi and Chief Minister Jayalalithaa is strictly condemnable."
"We may differ politically... In public life people are expected to maintain ethics," she said.