Jamiat Ulema-e-Islam-Sami's provincial president Maulana Yousuf Shah and former deputy speaker provincial assembly Ikramullah Shahid filed the petition on Monday.
The high court had passed an order in May declaring drone strikes a "war crime". However, drone strikes continue in tribal and adjoining areas.
The Prime Minister and secretary for the ministry of interior were named as respondents.
Defence Council of Pakistan (DPC) chairperson and Ulema-e-Islam-Sami (JUI-S) chief Maulana Samiul Haq said Peshawar, Islamabad and Karachi were not safe after the recent drone strike in Hangu.
DPC is a grouping of extreme right political parties and extremists groups. JuD chief and Lashkar-e-Taiba founder Hafiz Saeed is also part of it.
The petition stated the high court had on May 9 termed the drone strikes a "war crime" and against the sovereignty of the country. The court had directed the government to raise the issue at the United Nations (UN) and to seek compensation for victims of drone attacks.
"If drone strikes are not stopped through diplomatic channels then the federal government needs to shoot down the unmanned aircraft that has been violating the airspace of the country," the petition read, quoting the PHC's previous order.
It added seven months have passed since the order and any action by the federal government is yet to be seen.
"Innocent people are killed in drone strikes which also cause huge property losses to residents of the tribal areas," the Express Tribune quoted the petition as saying.
The Prime Minister, who is the chief executive of the country, is liable to contempt of court proceedings for not following clear orders of the PHC on drone strikes, it added.
It further stated that under Article 204, along with the PM, other concerned officials are also liable of contempt of court
"The DPC had filed a petition at the PHC on November 5, 2011, on which a comprehensive verdict was announced in May this year. The federal government, however, chose to ignore the order which is why contempt of court proceedings need to be initiated against them," said Samiul Haq.
The verdict further directed the government to take up the case in the United Nations Security Council. If the US uses its veto powers, an urgent meeting of the UN General Assembly be called to resolve the issue effectively.
It also stated in case all diplomatic channels fail to bring about the desired result, Pakistan must sever all ties with US and as a mark of protest deny it all logistic and other facilities within Pakistan.