The demand by the BJP and its partners was rejected by the RJD after a Legislature Party meeting held today and attended by party chief Lalu Prasad.
Chief Minister Nitish Kumar had called up RJD President Lalu Prasad last night, senior party leader Jagdanand Singh told reporters.
He, however, refused to divulge what transpired between the two during the telephonic talks.
Kumar has not commented so far on Friday's CBI raids in four cities in connection with a corruption case, in which the RJD chief, his wife Rabri Devi and son Tejashwi are among the accused.
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His silence has given rise to speculation of cracks in the Bihar's Grand Alliance government-- comprising JD(U), RJD and Congress.
Cancellation of the chief minister's weekly 'Lok Samvad' programme, which was scheduled for today, also added to the speculation.
Emerging from the RJD Legislature Party meeting, Finance Minister Abdul Bari Siddiqui told reporters, "The meeting praised Tejashwi Yadav's work as RJD Legislature Party leader."
Mundrika Prasad Yadav and Ramanuj Prasad, both RJD MLAs, were more forthcoming saying, there was no question of Tejashwi's resignation.
Lalu Prasad, Rabri Devi, Tejashwi and his minister brother Tej Pratap were present at the meeting with the legislators and other senior leaders of the party at the 10, Circular Road residence of former chief minister Rabri Devi.
Accompanied by RJD chief whip in the Assembly Lalit Yadav and senior party leader Jagdanand Singh, Siddiqui blamed the BJP and Prime Minister Narendra Modi for the action against Lalu Prasad and his family.
"The BJP and the PM are trying to fix Lalu Prasad with the help of government machinery," he alleged.
"But, whenever such a situation arises, the RJD has bounced back with double its strength," he said.
Siddiqui said the July 17 presidential election and the RJD's proposed rally in Patna against the BJP on August 27 were discussed at the meeting.
Lalu Prasad has claimed that Sonia Gandhi, Mamata Banerjee, Nitish Kumar, Mayawati, Akhilesh Yadav, Arvind Kejriwal and senior Left party leaders would attend the rally which would showcase the "unity" of the non-BJP parties before the Parliamentary election in 2019.