BJP minister Chandra Mohan Rai told the media that the 2010 mandate in Bihar was for the Janata Dal-United (JD-U) and the BJP to govern the state jointly.
"Nitish Kumar should resign as chief minister because people of the state gave the mandate to the NDA (National Democratic Alliance)," he said.
Another BJP leader and MP Hukumdeo Narain Yadav too made the same demand. "Nitish Kumar should resign and go for fresh elections (if the alliance breaks)."
The BJP demand came amid mounting tensions in the Bihar coalition following Nitish Kumar's objection to Gujarat Chief Minister Narendra Modi being projected as the prime ministerial candidate.
Modi's growing status in the BJP has not helped matters, with the Gujarat leader's supporters in the Bihar BJP gunning for Nitish Kumar.
The war of words is widely expected to lead to the snapping of 17 years of BJP-JD-U alliance.
Earlier today, Deputy Chief Minister Sushil Kumar Modi refused to meet Nitish Kumar, saying the issue of Narendra Modi needed to be taken up with the BJP national leadership.
A source close to the chief minister said Nitish Kumar had invited Sushil Modi and Road Construction Minister Nand Kishore Yadav of the BJP to discuss the political situation.
Yadav, also the state convenor of the NDA, admitted that he and Sushil Modi were invited by Nitish Kumar for discussions.
Till recently, Sushil Modi was considered not only close to Nitish Kumar but was an enthusiastic backer of alliance with the JD-U. He has changed his attitude.
BJP ministers in Bihar did not attend office the past two days.
JD-U leader and Bihar Education Minister PK Shahi reiterated that the BJP should clear its stand on Narendra Modi, who the party has named chief of the election campaign committee.
"It is not possible for JD-U to be part of an alliance under the leadership of Narendra Modi," Shahi said after meeting the chief minister.
Nitish Kumar on Thursday described the political situation in Bihar as "difficult".
All eyes are now on JD-U president Shard Yadav, who arrives here Saturday night and will hold meetings with Nitish Kumar and other party leaders.
One JD-U leader told IANS that the party had decided to snap its alliance with the BJP and that a formal announcement would be made on Sunday.