The move comes after comments of Chief Minister Jitan Ram Manjhi that Nitish Kumar would be the Chief Minister if the newly forged alliance secures a majority in next year's Assembly elections.
Seeking to play down the controversy, leaders of the alliance said their present priority was to win all ten seats in the bye-elections and the leadership issue would be decided after Assembly elections next year.
Leaders of the three parties said programmes were being chalked out for a joint rally of Lalu Prasad, Nitish Kumar and some senior Congress leader like its general secretary C P Joshi.
"The choice of Chief Minister of the alliance will be decided after the polls next year by senior leaders like Lalu Prasad, Nitish Kumar, Sharad Yadav and Sonia Gandhi," he said.
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Efforts would be made during the Assembly elections next year to expand the secular alliance by bringing more parties who are opposed to the BJP, Purbe said.
With Manjhi's comments about Nitish Kumar triggering an intense political debate, JD(U) Bihar chief Basistha Narayan Singh said there was no "bickering" among the allies on the topic as Manjhi had only stated the resolution of JD(U) Legislature party at the time of deciding the change of leadership in the wake of general election debacle.
"Manjhi made the comments in the context of his party JD(U), whose legislators had taken a resolution in May during change of Chief Minister, that the next Assembly polls will be fought under the leadership of Nitish Kumar," Singh said.