Officials from India's Ministry of External Affairs summoned Irish ambassador Feilim McLaughlin to discuss Dublin's response to the tragedy.
The young woman died from septicemia seven days after being admitted to hospital.
Her husband Praveen has said she was repeatedly denied an abortion despite the fact that the couple was told she was miscarrying.
She was 17 weeks pregnant when she went into hospital in Galway on October 21.
Her parents Mahadevi and Andanappa Yalagi are demanding that the Irish government amends its laws on abortion to ensure "no more lives are lost".
The news comes admid continuing tensions and mixed messages from the Taoiseach and Tanaiste on the issue of abortion legislation.
Enda Kenny said that he will not be rushed into passing legislation.
"This is a matter that has divided Irish society now for a great number of years and I'm not going to be rushed into a situation by force of numbers on any side.
"This is something that has to be treated rationally and openly and truthfully and that's what will happen."
Asked if he was concerned about the international coverage and diplomatic fallout from the case, Mr Kenny answered: "Well, no more than Irish citizens losing their lives in other countries which has happened in the past, this is always a matter of concern."
"Nobody set out for this to happen and as I say it's important that in the case of this particular tragic circumstance that we get to know the facts and the truth and the accuracy and the precision of what happened here so we can comment on the basis of factual evidence and not hearsay."
But the Taoiseach's caution was not shared by Tanaiste Eamon Gilmore, who is adamant that action is required.
The Labour minister held private talks with the Indian ambassador to Ireland, Debashish Chakravarti, who is understood to have expressed "deep concern" about Savita's death.
Mr Gilmore said that legal clarity was now needed on medical terminations, stating that doing nothing is "not an option".
Mr Gilmore's remarks were echoed by Health Minister James Reilly who said: "We owe it the citizens of this country and we owe it to the professionals that care for them to give them absolute clarity."