At a meeting of party workers today, while Mr Kumar hit out at the Congress, he also said he would attend the rally in Patna next month if invited, said party spokesman Sanjay Singh.
Mr Yadav's party, the RJD, has said it has already invited him publicly and the party chief will also invite him in person for the BJP hatao desh bachao (drive out the BJP and save the nation) rally.
Mr Kumar's support for the BJP candidate has been seen as a mark of his growing proximity with the BJP, triggering expectations of a political realignment in Bihar. His decision has drawn sharp criticism from both alliance partner Congress and Lalu Yadav.
The BJP's conspiracy allegations against Lalu Yadav and his family have been said to be a source of embarrassment for the Chief Minister and a key reason for the deterioration in ties. Mr Kumar however, has publicly shown support for Mr Yadav and challenged the BJP to prove its charges.
After the strong rumours of a split in the alliance, Mr Yadav had responded with two questions -- "Am I a fool?" and "Do I look like Kalidas?" -- indicating that he would not score a self-goal by splitting with Mr Kumar and bringing down the government.