The company has said it is taking the family's correspondence with the "utmost seriousness and humility".
Anna Sebastian Perayil, the 26-year-old Ernst and Young employee who allegedly died of "work-related stress", had raised concerns over work pressure with her seniors, her father Sibi Joseph has said.
"We advised her to quit, but she insisted that this stint would provide valuable professional exposure," Mr Joseph told reporters, adding that Anna used to work late into the night.
Mr Joseph claimed that Anna had earlier "complained to the assistant manager, but they insisted on working even at night".
The family, he said, is not planning to take legal action in the matter but hoped that others would not have to face similar circumstances.
"We do not want the newbies joining such corporate companies to face similar situations," Mr Joseph said.
Anna Sebastian, who worked at EY's Pune office for around four months, died in July. Earlier this month, her mother Anita Augustine wrote to EY India Chairman Rajiv Memani and flagged the "glorification" of overwork at the consulting firm.
"I am writing this letter as a grieving mother who has lost her precious child, Anna Sebastian Perayil. My heart is heavy, and my soul is shattered as I pen these words, but I believe it is necessary to share our story in the hope that no other family will have to endure the pain we are going through," she wrote.
She noted that her daughter was an excellent student and topped school and college, clearing the tough CA exam with distinction.
Congress leader and Thiruvananthapuram MP Shashi Tharoor, on Friday, said that he had a "deeply emotional and heartrending conversation" with Anna's father. He added that Anna died after a cardiac arrest, "following four months of deeply stressful seven-day weeks of 14 hours a day at Ernst & Young."
"He (Anna's father) suggested, and I agreed, that I raise the issue of legislating, through Parliament, a fixed calendar for all workplaces, whether in the private sector or the public, that would not exceed eight hours a day, five days a week,” Mr Tharoor wrote on X.
The Congress leader asserted that inhumanity at the workplace must be legislated out of existence "with stringent punishment and fines for offenders."
"Human rights do not stop at the workplace! Will raise this matter at the first opportunity during the next session of parliament," he added.
Amid public outrage, the Ministry of Labour and Employment said that it has taken up a complaint in the case and will investigate the circumstances that led to Anna's demise.
Minister of State for Labour, Shobha Karandlaje, wrote in post on X: "Deeply saddened by the tragic loss of Anna Sebastian Perayil. A thorough investigation into the allegations of an unsafe and exploitative work environment is underway. We are committed to ensuring justice & @LabourMinistry has officially taken up the complaint. @mansukhmandviya".
Issuing a statement, EY India said it was deeply saddened by Anna's death and is taking her family's correspondence with the "utmost seriousness and humility".
"While no measure can compensate for the loss experienced by the family, we have provided all the assistance as we always do in such times of distress and will continue to do so," it stated.