The JD(U), of which Kumar is the president, reciprocated by hinting that it would go with the opposition in the upcoming vice-presidential election.
Media reports said Gandhi intervened in favour of Kumar and instructed party leaders not to criticise the Bihar chief minister.
Bihar Congress president Ashok Choudhary confirmed to PTI that he had a meeting with Gandhi earlier this week in Delhi but refused to divulge what transpired there.
Gandhi was absent when the Congress-JD(U) spat broke out.
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The sparring began after senior Congress leader Gulam Nabi Azad attacked Kumar for breaking ranks with the opposition and supporting NDA's pick Ram Nath Kovind for the July 17 presidential poll.
He had alleged that Kumar wanted to ensure the defeat of 'Bihar ki Beti' Meira Kumar, who is the opposition's candidate for the poll.
People having one ideology take one decision while those with many ideologies take different decisions, Azad had said, apparently referring to JD (U)'s long association with BJP.
The JD(U) chief made it clear that his party was no "pichlagoo" (camp follower) of any party.
The war of words between the JD(U) and the Congress threatened the Grand Alliance government in Bihar, which includes the Congress and RJD of Lalu Prasad.
Kumar's bonding with Rahul Gandhi is well known in political circles.
It is also known that it was at Gandhi's intervention that the Congress had put pressure on Prasad to announce Kumar as the chief ministerial candidate on the eve of the 2015 Bihar Assembly poll.
She is scheduled to meet Congress and RJD legislators and parliamentarians. However, no meeting with chief minister Kumar has been fixed.
Reacting positively to the Congress gesture, JD(U) has hinted that it could side with the opposition in the August vice-presidential poll.
"If our party is invited to participate in a meeting of the opposition to discuss the issue of vice-presidential election, we will certainly attend," JD(U) national spokesman K C Tyagi told PTI over phone.
Asked who would represent JD(U) in the proposed opposition's meeting, Tyagi said that it would be decided by Kumar and senior party leader Sharad Yadav.
Choudhary, who is also the education minister in the Nitish Kumar-led government, told PTI, "We expect JD(U) would be with us in the vice-presidential poll.