Mr Higgins called for "some form of investigation" which meets the needs of the public, family and State.
Speaking in Brussels, Mr Gilmore stood by the President saying he was "reflecting the national mood" and had not crossed the Constitutional line of his role.
"I think the President was reflecting what is the national mood. That is the President's role," he said.
Mr Gilmore said President Higgins had not crossed the line and his predecessors had similarly expressed views on issues.
Earlier, Michael D Higgins has said his intervention in the row over an inquiry into the death of an Indian dentist after a miscarriage showed solidarity with the people.
Defending his remarks, Mr Higgins said his position was very straightforward as he was expressing the great sadness felt in Ireland over Savita Halappanavar's hospital death.
"I said that it was a great tragedy, a young woman, and I expressed my sympathies to her husband and her extended family," he said.
"I was joining the thousands of Irish people who are on the streets saying the same thing and then, on the specific issue where do we go from here, I said it's very important that the investigation be such as satisfies the genuine concern of the Irish people and that meets, in some way - in some small way - helps reducing the grief for Savita's husband and her family and then that meets the needs of the state's responsibilities.
"It was no more and no less than that."