Mr Abdullah said the Centre needed to deal with the matter at once, "otherwise, this (protests) will blow out of proportion and then it will be difficult to control".
National Conference patron Farooq Abdullah on Wednesday asked the Modi government to deal with the situation arising out of suicide by a Dalit scholar at Hyderabad Central University "at once" and warned that otherwise the situation could become difficult to control.
"It is a tragedy for us. I think the central government should get it (the matter) investigated at whatever authority and whatever level they want to," Mr Abdullah told reporters in Jammu.
"It must be investigated immediately so that the heartburn across the nation among the young students comes to rest (sic)," the former Jammu and Kashmir Chief Minister said.
Mr Abdullah said the Centre needed to deal with the matter at once, "otherwise, this (protests) will blow out of proportion and then it will be difficult to control".
Rohith Vemula was found hanging in a hostel room on the varsity campus on January 17.
He was among five research scholars who were suspended by the varsity in August last year and also one of the accused in the case of assault on a ABVP leader.
Union Labour Minister Bandaru Dattatreya and the Hyderabad University Vice Chancellor were on Tuesday named in an FIR over the alleged suicide by the student.