Responding to a question on the demand for his resignation, Tejashwi Yadav told reporters outside the Assembly, "It (resignation demand) is only in the media."
Mr Yadav had skipped an official function on July 15, in where he was top share dais with Chief Minister Nitish Kumar, triggering speculation that the festering acrimony between the JD(U) and the RJD had reached a flash point in the wake of a FIR being registered by the CBI against the deputy chief minister in the land-for-hotels case.
RJD president Lalu Prasad has also ruled out the resignation of his son Tejashwi. While Tejashwi Yadav appeared to have decided to dig in his heels, BJP leader Sushil Kumar Modi said, "He has only two options - either tender resignation or get sacked."
Mr Modi, who is the state BJP Parliamentary Party chief, urged Nitish Kumar to "stand firm on his ground (in seeking resignation of Tejashwi)... The BJP will be standing with him on his decision on this issue".
Though none of the JD(U) spokesmen made any statement on the issue today, party MLA Shyam Bahadur Singh said, "It's better if the alliance breaks today... We love to work with the BJP."
Congress MLA Shakil Ahmad Khan and MLC Dilip Chaudhary suggested senior leaders of the three coalition partners to talk among themselves to hammer out a solution.
Nitish Kumar heads a three-party coalition government which also includes the Congress.
Amid reports of the BJP going soft on the chief minister since the Tejashwi episode came to the fore, Mr Modi thanked him for his support to NDA's presidential pick Ram Nath Kovind.
"Nitish Kumar's support to the NDA nominee holds a lot of significance for which we thank him," he said, claiming along with NDA and JD(U) MLAs, four Independents also voted for Mr Kovind.
Tejashwi Yadav, who was accompanied by RJD chief whip in the Assembly Lalit Yadav, also claimed 100 per cent voting by the RJD and Congress MLAs in favour of UPA's president nominees Meira Kumar.
Three CPI(ML) MLAs have also voted for Mr Kumar.