Mengal further demanded that Pakistan should be tried for genocide of the Baloch people in the International Court of Justice as well. In April this year, a Pakistani military court found him guilty of spying and sentenced him to death.
The case - a rare foray for the two nations into the global courts - has highlighted the recent sharp upsurge in tensions between the nuclear-armed rivals.
India argues Jadhav was wrongly convicted for spying, while Pakistan says his legal process is ongoing and Pakistan has met its obligations under the Vienna Treaty on Consular Relations.
"Pakistan's security is so important and we have to maintain our fundamental sovereign right", Sartaj Aziz said.
Jadhav was arrested on March 3, 2016, through a counter-intelligence operation in Balochistan's Mashkel area for his involvement in espionage and sabotage activities against Pakistan. However, India maintains that he was kidnapped from Iran where he had business interests after retiring from the Indian Navy.
The court said Pakistan had indicated that the execution would probably not take place before August 2017.
Pakistan attended the hearing at the ICJ "because of its conviction that the only way to resolve all outstanding issues is through peaceful means", it said.
New Delhi welcomed the court's unanimous decision on Jadhav, while Islamabad said it had informed the ICJ that it did not accept the court's jurisdiction in matters related to national security.
Reacting to the order of the International Court of Justice (ICJ) in the Kulbhushan Jadhav case on Thursday, Pakistan said it will not accept the United Nations court's jurisdiction in matters related to national security.
Supporters hold posters of former Indian naval officer Kulbhushan Jadhav and light fire crackers as they celebrate the International Court of Justice order on Jadhav, in Ahmadabad on Thursday.
There has also been criticism over why Pakistan accepted the global court's jurisdiction in the first place.
"India has the right to seek consular access for Jadhav", he added.
Yesterday, International Court of Justice stayed the execution of Kulbhushan Jadhav till its final decision. The ruling came three days after India and Pakistan gave their submissions in the case. It said Pakistan's alleged failure to provide consular access to Jadhav appeared to be falling within the scope of the Vienna Convention.