Justice Vibhu Bakhru, however, asked petitioner Uber India Systems Pvt Ltd to give its representation to Delhi government's transport department on December 29.
The court also declined Uber's request that it should be granted the relief in parity with the OLA cab, which has been allowed to operate in the Capital for the time being.
"It is not identical. The person pays to the taxi person there and in your case the payments are accepted through other mode. We are not staying the order, but we would like them (Delhi government) to hear you.
The court, meanwhile, has kept pending the petition and listed it for further hearing on January 6, 2015.
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It also said that the Uber India system shall provide necessary contact details including e-mail addresses on which the communication in this regard be sent.
The court order came on a plea moved by Uber, through senior counsel Rajiv Nayar, who sought quashing of the public notice issued on December 8 blacklisting Uber from providing any transport service in the national capital.
"It is well settled that no order of blacklisting can be sustained without an opportunity being given to be heard by the affected party," Nayar argued.
Uber moved court after the High Court yesterday allowed OLA Cabs to operate in the capital city until further notice.
Besides Uber, 20 other app-based cab services including Ola Cabs have been banned to operate within Delhi, following the rape of a 27-year-old woman executive on December 5 night by the driver of Uber, the US based app-based cab operating service.