This came a day after India approached the International court of Justice seeking reversal of Military court order.
The death sentence was issued to Jadhav, who was a retired Navy officer, last month.
India, in its appeal to the ICJ, accused Pakistan of "egregious" violations of the Vienna Convention on Consular Relations and asserted that Jadhav was kidnapped from Iran where he was involved in business activities after retiring from the Indian Navy but Pakistan claimed to have arrested him from Balochistan on March 3, 2016.
Reacting to the development, External Affairs Minister Sushma Swaraj said, "I have spoken to the mother of Kulbhushan Jadhav and told her about the order of President, ICJ under Art 74 Paragraph 4 of Rules of Court."
Swaraj said senior advocate Harish Salve was representing India before the ICJ in the Jadhav case.
ICJ President Ronny Abraham has reportedly written a letter to Pakistan government, asking it to act in such a way which would enable the implementation of any order the ICJ may issue in the case.
India, in its appeal, contended that it was not informed of Jadhav's detention until long after his arrest and that Pakistan failed to inform the accused of his rights.
It further asserted that, in violation of the Vienna Convention, the Pakistani authorities were denying India its right of consular access to Jadhav, despite repeated requests.
"Referring to 'the extreme gravity and immediacy of the threat that authorities in Pakistan will execute an Indian citizen in violation of obligations Pakistan owes to India', India urges the Court to deliver an order indicating provisional measures immediately, 'without waiting for an oral hearing'," India's appeal said.
Jadhav, 46, was given death sentence last month by the Field General Court Martial in Pakistan, evoking a sharp reaction in India which warned Pakistan of consequences and damage to bilateral ties if the "pre-meditated murder" was carried out.
In its application, India had also informed the ICJ that it learned about the death sentence against Jadhav from a press release.
"India claims that 'linking assistance to the investigation process to the grant(ing) of consular access was by itself a serious violation of the Vienna Convention'," the ICJ release said.
The ICJ said India urged it to restrain Pakistan from carrying out the death sentence, and direct Islamabad to take steps to annul the decision of the military court.
Pakistan claims its security forces had arrested Jadhav from the restive Balochistan province on March 3 last year after he reportedly entered from Iran. It also claimed that he was "a serving officer in the Indian Navy."
Jadhav was sentenced to death for "espionage and subversive activities".
India acknowledges that Jadhav had served with the Navy but denies that he has any connection with the government.