The delay in finalising the report into the death of Savita Halappanavar has been raised at a meeting of the HSE West Regional Health Forum.
Ms Halappanavar, who was 17 weeks pregnant, died at Galway University Hospital following a miscarriage last October.
Chief Operating Officer of the hospital group Tony Canavan told the meeting that the chairman of the inquiry team, Professor Sabaratnam Arulkumaran, was continuing to work on the report.
He said every effort was being made to complete the task as soon as possible.
Mr Canavan said he hoped to be in a position to present a draft of the final report to Ms Halappanavar's husband Praveen by this Friday.
He said the process of preparing such a detailed report required a number of drafts, which had to be checked and rechecked.
Mr Canavan said the HSE wanted to give Mr Halappanavar every possible opportunity to co-operate with the inquiry, as his involvement would improve the process and mean it was better informed.
He said the hospital was doing everything it could to co-operate with the inquiry.
The Chairman of the HSE West Regional Health Forum said it was not good enough that the process had not yet been completed.
Councillor Pádraig Conneely said the delay in finalising the inquiry was unacceptable and that it should have been conducted in a more timely manner.
Cllr Conneely said the eyes of the world were on Galway University Hospital and its maternity unit.
He said it was in everyone's interest that the report was fully completed.
He urged Mr Halappanavar's legal representatives to co-operate with the review.
This call was echoed by Mr Canavan.
At last month's meeting of the forum, members were told the draft report had been furnished to parties named in the report and that it would soon be finalised.
This afternoon, Mr Canavan said there was no set completion date and no indication as to when the report would be presented to the minister or when it would be made public.
Mr Halappanavar's solicitor has said his client will review the draft HSE report into the circumstances surrounding his wife's death but is not likely to co-operate further with the inquiry process.
Gerard O'Donnell said his client will consider the report and then decide as to whether he will meet with the chairman of the inquiry team.
Other than that, Mr Halappanavar is unlikely to partake in the review process, he said.
The inquest into the death of Ms Halappanavar is due to resume in Galway on 8 April.