In a statement released post midnight, the Pakistan foreign office said it has informed Jadhav of his rights to consular access under the Vienna Convention.
However, the statement said that Pakistan will grant consular access to Jadhav "according to Pakistani laws".
"As a responsible state, Pakistan will grant consular access to Commander Kulbushan Jadhav according to Pakistani laws, for which modalities are being worked out," it said.
The move comes after the ICJ rapped Islamabad for continually denying Jadhav, incarcerated in a military jail in an unknown location in Pakistan, consular access in accordance with the Vienna Convention.
India on Thursday had asked Pakistan to "act immediately" on the ICJ verdict and grant consular access to Jadhav.
The ICJ has directed Pakistan for continued stay on the death sentence of Jadhav and to provide him consular access. Pakistan had refused to allow Indian officials to meet Jadhav ever since his "arrest" in March 2016 for alleged espionage. India had approached the ICJ after he was in April 2017 sentenced to death by a military court.
Islamabad's move comes ahead of Pakistan Prime Minister Imran Khan's visit to Washington, where he is to meet President Donald Trump at the White House on July 22.
Pakistan also arrested Mumbai attacks mastermind and Jamat-ud-Dawa chief Hafiz Saeed on Wednesday, in another move ahead of the Imran-Trump meeting.
While acceding to the ICJ ruling on Jadhav, Pakistan has maintained that it will "proceed as per law".
The Foreign Office said after the ICJ ruling: "Having heard the judgment, Pakistan will now proceed as per law", which was also echoed by Imran Khan in his tweet on Thursday.
"(I) appreciate ICJ's decision not to acquit, release & return Commander Kulbhushan Jadhav to India. He is guilty of crimes against the people of Pakistan. Pakistan shall proceed further as per law," the Pakistan Prime Minister tweeted.
Ministry of External Affairs spokesperson Raveesh Kumar on Thursday said that India expects Pakistan to "act immediately" on the ICJ ruling and allow consular access to Jadhav.
"When the court says immediate action, it means 'immediate' and Pakistan should take immediate action. We are waiting for Pakistan to act," he had said.
Kumar said the ICJ in its verdict ruled that Pakistan "should take all measures to provide for effective review and reconsideration of the conviction and sentencing of Jadhav, and that this should include enacting appropriate legislation".
( With inputs from IANS )