Rai, who recently underwent a surgery and is currently undergoing physiotherapy at the Indian Spinal Injuries Centre, had earlier on Friday met Chief Minister Arvind Kejriwal and requested that he be relieved of his responsibilities.
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Delhi's PWD and Health Minister Satyendra Jain has been asked to take charge of the Transport Department.
Rai's resignation comes just days after his name cropped up in connection with allegations of corruption in the city government's app-based premium bus service scheme.
Bharatiya Janata Party (BJP) legislator Vijender Gupta had reportedly filed a complaint was with the Anti-Corruption Bureau (ACB), alleging that the AAP Government was favouring an aggregator with regard to the premium bus service scheme and no norms had been followed.
Rai had earlier said that he was "ready to go to jail" if corruption was proven against him in the bus service scheme.