His resignation was accepted by Rajasthan Governor and university Chancellor Kalyan Singh, officials said.
The resignation came a day before a hearing scheduled in the Rajasthan High Court on the controversial appointment of Singhal, who was appointed as VC of the University in August 2015.
The Chancellor on the advice of state government has given the additional responsibility of the VC to Jaipur divisional commissioner Rajeshwar Singh, a release from the Governor House said.
The court had not pronounced its verdict in the case during its last hearing on January 4 and deferred it till January 9.
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The double bench of the court comprising justices K S Jhaveri and Vineet Kumar Mathur had heard the PIL filed by former judge of High Court I S Israni and others challenging Singhal's appointment.
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Later, Health and Medical Education Minister Kalicharan Saraf said that former VC of Rajasthan University Dev Swarup, who was appointed during Congress regime, too was not a Ph.D degree holder.
There were many VCs who did not hold Ph.D degree, but they still worked for the society and did excellent work, he said and asked why Congress has problems with Singhal.
Saraf said Rajasthan University fulfils all the criteria to become a Central University and the matter will be taken up with the central government.