Kumar tendered his resignation yesterday citing it was his "duty to take moral responsibility" for the results.
A large number of supporters of Kumar are heard asking MLAs to choose only him as the legislature party leader and putting pressure on Kumar to withdraw his resignation.
Minister Lessi Singh told reporters before getting inside the residence that apart from Kumar nobody else would be accepted for the post of chief minister.
"We got a mandate in 2010 in the name of Nitish Kumar only and hence nobody else can head the government. If Kumar does not reconsider his decision to take back the resignation, we will also resign," she said.
Ministers Shyam Rajak and Nitish Mishra also dismissed the possibility of anybody replacing Kumar as the chief minister. MLA Ajit Kumar, Anil Kumar and others echoed similar views.
JD(U) President Sharad Yadav, who had to face the ire of agitated Kumar supporters, who claimed to see him (Yadav) behind his resignation, remained inside Kumar's official residence since afternoon.
Senior minister Narendra Singh, considered an alternative, has denied being in the race for CM and said he would propose the name of Kumar to continue as CM.