In his petition filed yesterday, Communist Party of Pakistan chairman Jameel Ahmed contended that Pasha was not eligible to hold the high post.
He based his petition on articles in the foreign media which said Pasha had allegedly sought and received approval from Arab leaders to sack President Zardari.
"Till date these allegations have not been denied by both the ISI Director General and the Inter-Services Public Relations," Ahmed said.
He requested the apex court to declare that Pasha's continuance in office was in direct contravention of Article 244 of the Constitution, which deals with the oath of the armed forces.
As interim relief, the court should direct the federal government to suspend the ISI chief till the disposal of the petition, Ahmed said.
Controversial Pakistani-American businessman Mansoor Ijaz has claimed that Pasha visited several Arab countries to seek approval for the ouster of Zardari after the May 2 US raid that killed Osama bin Laden in Abbottabad.
Ijaz also made public the alleged memo in which US help was sought to prevent a feared coup in Pakistan after the killing of bin Laden.
Ahmed said in his petition: "If whatever stated by Mansoor Ijaz about the 'memogate' is correct, then what about his opinion concerning the ISI (DG) that he got approval from the Arab world for the removal of the President."
He added: "This is alarming and shows involvement of the ISI DG." Ahmed contended that Pasha's alleged meetings with Arab leaders certainly came under the purview of politics.
Prime Minister Yousuf Raza Gilani has had to face embarrassing questions from the media on whether Pasha had sought his permission to visit Arab countries in the aftermath of the raid against bin Laden.
Bushra Gohar, a senior leader of the Awami National Party, which is part of the ruling coalition, has demanded that the ISI chief should resign following Mansoor Ijaz's revelations.
Shortly after the US raid in Abbottabad, Pasha had secretly visited China, Saudi Arabia and some other countries.