The seer was found hanging by disciples at Baghambari Muth in Allahabad on Monday.
The Uttar Pradesh Police today constituted an 18-member SIT to probe the death of Akhil Bharatiya Akhada Parishad president Mahant Narendra Giri and detained a disciple of the seer in Haridwar.
Meanwhile, Chief Minister Yogi Adityanath said all aspects related to the death are being investigated and the guilty will not be spared.
Deputy Chief Minister Keshav Prasad Maurya too said his government is ready for every kind of investigation into the matter.
Samajwadi Party chief Akhilesh Yadav has demanded a judicial probe by a sitting high court judge.
A plea seeking a CBI probe into the death was also sent to the Chief Justice of the Allahabad High Court.
The seer, who was the president of the largest organisation of sadhus in India, was found hanging by his disciples at Baghambari Muth in Allahabad on Monday.
An alleged suicide note was also found, in which the seer had written that he was mentally disturbed and upset with one of his disciples, police had said.
According to a release, the 18-member Special Investigation Team (SIT) constituted by Allahabad SSP will include two circle officers.
Meanwhile, ADG (Law and Order) Prashant Kumar in Lucknow said the state police detained the seer's disciple Anand Giri on Monday night in Haridwar.
Anand Giri was detained after a case for abetting suicide was lodged against him, Mr Kumar said.
The ADG said in the suicide note, names of three people were mentioned and on the basis of the FIR, Anand Giri was detained.
"He is being brought to Allahabad for further probe," he said, adding that evidence in the case is being collected.
An "unbiased and transparent" probe into the matter is on and the state police is capable of handling the case, the officer said.
About the veracity of the suicide note, Mr Kumar said forensic experts are looking into it.
Chief Minister Adityanath, who rushed to Allahabad to pay his respects to the seer, told reporters that the case will be solved soon.
Every single aspect connected with the case will be exposed and the guilty will be punished, he added.
Deputy Chief Minister Keshav Prasad Maurya, who paid floral tributes to the mahant, said the guilty will not be able to escape and his government is ready for every kind of probe, be it by police or the CBI.
Samajwadi Party President Akhilesh Yadav on Tuesday demanded a judicial probe by a sitting high court judge.
The former Uttar Pradesh chief minister also visited Baghambari Muth in Allahabad and paid homage to the seer.
Meanwhile, a lawyer, Sunil Choudhary, mailed a petition to the Chief Justice of the Allahabad High Court, seeking a CBI probe into the case.
Mr Choudhary said according to some news portals, a high-rank UP police officer and land mafia were involved in the case.
The probe must be transferred to the CBI and the state government be directed to suspend the Allahabad district magistrate and the SSP, the petition added.