Pakistan last week said it will allow 46-year-old Mr Jadhav to meet his wife, months after India had requested Islamabad to grant a visa to his mother on humanitarian grounds.
During his weekly media briefing, Foreign Office spokesperson Mohammad Faisal said Pakistan was awaiting India's response on the offer.
Mr Jadhav, a former Indian Navy officer, was sentenced to death by a Pakistani military court in April on charges of espionage and terrorism. The International Court of Justice in May halted his execution on India's appeal.
Pakistan has repeatedly denied India consular access to Mr Jadhav on the ground that it was not applicable in cases related to spies.
Some media reports have linked Pakistan's offer to the quiet efforts by the US.
Pakistan, however, insisted that the offer was made purely on the humanitarian grounds.
Mr Jadhav has filed an appeal with Pakistan Army chief Gen Qamar Javed Bajwa to seek clemency, which is still pending.
Pakistan claims its security forces arrested him from restive Balochistan province on March 3 last year after he reportedly entered from Iran.
However, India maintains that Mr Jadhav was kidnapped from Iran where he had business interests after retiring from the Navy.
Mr Jadhav's sentencing had evoked a sharp reaction in India.
After India approached the ICJ, a 10-member bench on May 18 restrained Pakistan from executing Mr Jadhav till adjudication of the case.
The ICJ has asked Pakistan to submit its response or memorial by December 13 before the court could start further proceedings in the case.
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