"Instead of pressurising the Governor or issuing empty threats, Stalin can bring no-confidence motion," senior BJP leader H Raja tweeted.
"Why he is afraid of it?" he asked in the same tweet.
The BJP National Executive member's comments come a day after Stalin-led the opposition to Raj Bhavan.
He had urged the Governor to direct the state government to prove its majority in the assembly within a week, in the wake of the revolt by 19 AIADMK MLAs against the Chief Minister last month.
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The revolt by 19 AIADMK MLAs came a day after the merger of the factions led by Palaniswami and former chief minister O Panneerselvam.
Delegations of DMK, Congress and Left parties had already called on the governor and pressed for a floor test for the Palaniswami government.
Last week, sidelined AIADMK leader TTV Dhinakaran had met Rao and sought replacement of Palaniswami, who, however, had been asserting that his government had the requisite majority and none could topple it.
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