The judicial body of the United Nations had earlier fixed time limits for the filing of the initial pleadings in the case.
"India has today (Wednesday) submitted its memorial to the International Court of Justice in the Jadhav case involving egregious violation of Vienna Convention on Consular Relations 1963 by Pakistan. This is in furtherance of our application filed before the court on May 8, 2017," Indian Ministry of External Affairs Spokesperson Raveesh Kumar said.
The court had fixed June 13, September 13 and December 13 as dates for India to file its documents and for Pakistan to file counter-documents. The order was made after taking into account the views of the parties, said an ICJ statement.
Jadhav was awarded capital punishment by a Pakistani military court for espionage.
India challenged the verdict in the top UN court, accusing Pakistan of violating the Vienna Convention by failing to provide Jadhav with consular access which it said was in breach of international human rights laws.
Delhi also appealed to the court to impose emergency measures for Jadhav's execution to be suspended until the legal battle in The Hague concludes.
On May 18, the ICJ ruled that Jadhav must not be put to death by Islamabad until the ICJ has had enough time to pass the final judgement in the case, and ordered a stay against the execution.
Pakistan says Jadhav was arrested during a counter-intelligence raid in Balochistan in March 2016.
He "confessed" to being a spy for India's Research and Analysis Wing (RAW) in a video released by Pakistan.
"I welcome the ICJ verdict. My thoughts tonight are with Kulbhushan Jadhav, alone in a prison cell in Pakistan and with his distraught family for whom this verdict brings a rare moment of relief, joy & renewed hope, that he will one day be free to return his home in India," the outgoing Congress President said in a tweet.
His remarks came after ICJ put on hold the death sentence to Jadhav by a Pakistani military court for alleged espionage.
The ICJ also accused Pakistan of denying India consular access to Jadhav, saying it has not only violated the Vienna Convention on diplomatic relations, but has also ignored a 2008 bilateral agreement on consular access.
However, the ICJ in its verdict has decided not to acquit or release Jadhav.
In November 2008, India and Pakistan inked a bilateral agreement on consular access to prisoners of their countries.
India moved the ICJ on May 8, 2017 after a Pakistani military court sentenced Jadhav to death for alleged espionage.
The world court said the dispute was related to the "interpretation and application of the Vienna Convention on Consular Relations". The ICJ said it has "jurisdiction under Article I of Optional Protocol to Vienna Convention on Consular Relations concerning the Compulsory Settlement of Disputes".
The first objection of Pakistan to the admissibility of India's application was on "alleged abuse of process". The court observed that there was "no basis to conclude that India abused its procedural rights when it requested indication of provisional measures -- Articles II and III of Optional Protocol do not contain preconditions to the Court's exercise of its jurisdiction."
The second objection was on "alleged abuse of rights" and Pakistan's "contention that India failed to prove Jadhav's nationality". The ICJ said there was "no room for doubt that Mr. Jadhav is of Indian nationality".
The other arguments advanced by Pakistan "based on alleged breaches of India's international obligations under Security Council resolution 1373 (2001)" were also rejected.
The third objection of Pakistan was on "India's alleged unlawful conduct". The court said Pakistan's objection based on "clean hands" doctrine (a rule of law that a person coming to court with a lawsuit or petition for a court order must be free from unfair conduct) was rejected.
It said there was "no explanation on how alleged unlawful conduct by India prevented Pakistan from providing consular access to Jadhav.
Pakistan's objection based on the principle of "ex turpi causa non oritur actio" (that no action can arise from an illegal act) cannot be upheld, the ICJ said.
The principle "ex injuria jus non oritur" (law or right does not arise from injustice) implies that "unjust acts cannot create law" is inapposite in the present case, the court said while throwing out Pakistan's third objection to admissibility of India's petition.