The LJP chief assured that his party would take due care of the "worries" of Muslim, Dalit and deprived sections with respect to NRC.
The rebel legislators were disqualified by the then speaker K R Ramesh Kumar in July earlier this year under the anti-defection law after they tendered their resignation.
Nitish Kumar said the party will fight the next Assembly election with BJP and Union Minister Ram Vilas Paswan-led Lok Janshakti Party (LJP) in Bihar.
By-polls in five assembly constituencies were conducted in Bihar on October 21 which saw Rashtriya Janata Dal (RJD) winning two seats and Janata Dal (United) and AIMIM winning one seat each on Thursday.
Bihar's Water Resources Minister Sanjay Jha congratulated Kumar on his re-election and expressed the hope that under his guidance, the party will retain power in the elections.
Shah had triggered a political row on Saturday when he had said that it is important the country had one language reflecting its identity and only Hindi could unite the country.
Hitting out at Nitish, the RJD leader said if he was batting so well then why he asked for votes in the name of Prime Minister Narendra Modi instead of his work.
The trust vote is scheduled for tomorrow after the House was adjourned in the wake of the Assembly failing to meet the two deadlines set by Governor Vajubhai Vala to complete the trust vote on July 19.
The 13-month-old Congress-JDS government slumped into a minority earlier this month following the resignation of several dissident MLAs.Sixteen MLAs from the ruling coalition, including 13 from Congress and three JD(S) MLAs, have resigned from the cabinet.
The Assembly was debating a confidence motion moved by Chief Minister HD Kumaraswamy that came in the wake of several resignations submitted by Congress-JD(S) MLAs.