The tragic woman's husband has hit out at the team appointment to inquire into her death.
Praveen Halappanavar said he does not want employees of the hospital where Savita died to be part of the HSE probe.
"I will basically request that there be no-one from Galway on it," he said.
However, Social Protection Minister Joan Burton has said the Government will not rule out a public inquiry into the death of Savita Halappanavar, but insisted the HSE investigation must take place first.
Ms Halappanavar died at a Galway University Hospital on October 28 after allegedly being denied an abortion.
Mr Halappanavar is set to request that Prof John J Morrison, a consultant in obstetrics and gynaecology; Dr Catherine Fleming, consultant in infectious diseases; and Dr Brian Harte, consultant in anaesthesia and intensive care at Galway University Hospital, be removed from the HSE inquiry.
Praveen's solicitor Gerard O'Donnell said: "I have written to the Health Minister James Reilly in which the family has demanded a full public inquiry into Savita's death -- nothing less than a full public inquiry will suffice."
Mr Halappanavar said he wanted "...a fully independent inquiry so that the truth will come out."
This morning Education Minister Ruairi Quinn failed to back calls from Savita's husband for a fully independent inquiry, adding: "I would really hesitate to comment on calls for an independent inquiry.
"I think in the first instance people directly involved along with outside experts should look at what has happened."