Members of CPI and CPI (M) staged a protest outside the office of SEC here, alleging that a CPI candidate was not allowed to file nomination in Puthukottai District.
CPI (M) MLA K Bhimarao said the ruling AIADMK should not treat the SEC as one of its district units.
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"They have to announce dates afresh for receiving nominations and provide adequate time for campaigning, which alone would mean that the SEC is acting properly. Else this is an undemocratic action," he told reporters.
Later, the Left activists were detained by police for trying to stage a picketing of the SEC office.
Meanwhile, BJP, which announced its candidates for the by-polls, suffered a setback with the party's Tirunelveli Mayoral candidate Vellaiammal withdrawing her candidature.
Her move has paved way for AIADMK candidate E Bhuvaneswari's election unopposed as only these two candidates' nomination papers had been approved.
Responding to the development, party's state unit President Tamizhisai Sounderrajan alleged that her party candidate had been 'threatened' to withdraw nomination.
"We are strongly condemning it. She has been threatened by the opposite party" to withdraw nomination, she said in an apparent reference to AIADMK.
The SEC had come under flak from opposition parties, including DMK, which have accused it of being biased towards the AIADMK in the conduct of the by-polls to vacant local body posts, including that of three Mayors.
DMK is boycotting the polls.