Making the announcement at a press conference here, Kumar said he would stake his claim to the party's symbol -- ceiling fan -- as his faction represented the "real" Rashtriya Lok Samta Party.
He claimed to have support of Lalan Paswan, one of the party's two MLAs in the Bihar Assembly, and appointed him as its state unit president.
Kumar said he would continue to be part of BJP-led NDA.
"We are the original RLSP, not the one which Kushwaha claims (to lead). Today we have also made several appointments of the party's office-bearers," Kumar said.
The RLSP, a majority of whose leaders had moved away from JD(U), contested the 2014 General Election and 2015 Assembly polls in Bihar with the BJP.
Earlier, in August this year, Kushwaha had suspended Arun Kumar and Lalan Paswan from the party.
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