The move by Kumar, who has been elected as the new JD(U) Legislature Party Leader in place of Chief Minister Jitan Ram Manjhi, came after he questioned the "delay" by Governor Keshari Nath Tripathi in defusing the political crisis.
Kumar and MLAs supporting him landed in Delhi in two commercial flights.
Sources in the Rashtrapati Bhavan said the President will decide tomorrow on Kumar's plea to present supporting MLAs before him.
"It is more than 24 hours and no decision has come from the Bihar Governor in regard to our claim to form the government. The majority is in our favour and we will inform the President of India about it. We will take our MLAs to him around 2.15 pm tomorrow," Kumar told reporters at Patna airport.
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"We took the entire bunch of 130 supporting MLAs to Raj Bhavan, gave letters of support from all of them on February 8. Then what is there to study... There is no rationale in delaying the decision to invite me to form a government," he added.
Manjhi has sought a trial of strength by secret vote in the Assembly. The JD(U) has expelled him from the party for "anti-party" activities and the Speaker declared him an unattached MLA.
Besides about 99 JD(U) MLAs, Kumar has been accompanied by supporting RJD, Congress, Communist and independent legislators.
Kumar had met Tripathi yesterday to stake claim to form government while Manjhi, who also met the Governor later, refuted his former mentor's claim.
"The delay should not happen. We have staked our claim for government formation and given everything in writing to the Governor...We want that Constitutional values should be upheld and no wrong measures should be adopted for government formation," he added.