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"The situation is grave, it is urgent, and hence we approached this court at such short notice," senior lawyer Harish Salve, representing India, told the UN court, urging that Mr Jadhav's death sentence be suspended immediately.
Pakistan, said Mr Salve, had repeatedly denied consular access to India and no document of Jadhav's trial process was given by Islamabad.
Describing Mr Jadhav's trial as "farcical" and without a shred of evidence, Mr Salve said he was given a lawyer when the trial was nearly over. "The basic rights of Jadhav were thrown to the winds," he said.
Pakistan rebutted the allegations, accusing India of using the world court as a "political theatre".
Pakistan said Mr Jadhav's passport bears a Muslim name and India had been unable to explain it.
India argued that Pakistan violated the Vienna Convention by denying India consular access to Mr Jadhav 16 times and denying him the right to defend himself. Pakistan said "the Vienna Convention provisions did not apply to a spy involved in terror activities".
Last week, after India challenged the death sentence, Pakistan was asked by the International Court to put it on hold. Pakistan on Monday alleged that calling it a "stay order" was India's "manoeuvre".
India has not approached the international court on any case related to Pakistan since 1971, but the government has said it had no choice as the life of an Indian citizen is at stake.
Mr Jadhav, 46, arrested in March last year by Pakistan, was held guilty by the country's military court of spying and subversive activities. India says that Mr Jadhav was kidnapped from Iran, where he was running a business after retiring from the Navy.
India wants the international court to annul Mr Jadhav's death sentence and ensure that Pakistan does not act against the rights of India or of Mr Jadhav.
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