Kumar made the request to Gehlot over telephone, sources in the CM's office here said.
They said the Rajasthan CM assured Kumar that lawful action will be initiated against perpetrators of the crime against an 11 year-old girl hailing from Darbhanga who was gangraped allegedly by six persons in Rajasthan four months back and thrown on the road.
The girl is presently recuperating in a hospital in Jaipur after undergoing nearly a dozen operations.
Earlier, emerging from a function where Tibetan spiritual leader the Dalai Lama unveiled a statue of Lord Buddha, Kumar told reporters that he would urge his Rajasthan counterpart to shift the victim girl from general ward to provide special medical care.
He said he would also seek adequate security to the family of the victim.
The Bihar CM said that an official from the state with an aide would be present in the Jaipur hospital to provide assistance, including monetary benefit for speedy recovery of the victim.
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Kumar said his office would be constant touch with authorities in Rajasthan to monitor the health condition of the minor girl.
On instruction of Chief Minister Nitish Kumar, Deputy Resident Commissioner of Bihar in Delhi, Vipin Kumar, had gone to Jaipur to see the girl.