Petrol shortages hit Pakistan about 10 days ago and still long queues of cars and motorbikes were seen in front of the fuel stations despite official announcements that enough oil was available in the country.
Tehreek-e-Insaaf Information Secretary Shireen Mazari said the petrol crisis showed that Sharif was unable to run the country.
"The prime minister and his cabinet should resign and there should be fresh elections," she told reporters here.
She accused Sharif and his ministers of enjoying perks and privileges without caring for the sufferings of the people.
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"The government has done nothing regarding the implementation of the National Action Plan (NAP), except conducting meetings," she said.
The party last month ended more than four month long sit-in before the parliament seeking Sharif's ouster over alleged electoral fraud.
It is still demanding probe into the rigging.