Mr Halappanavar told the Herald that he will only cooperate with an independent inquiry, adding: "I have no faith in the HSE. Savita died in the care of the HSE."
The HSE probe has now been plunged into disarray with strong pressure mounting on Minister Reilly to transfer it into the hands of independent experts.
The latest controversy comes after the State agency asked the three Galway hospital staff to step down from the inquiry team following objections from Savita's family.
But a spokesman for the Health Minister this morning defended the probe and told the Herald that there is "no plans" for a public inquiry.
"It is still the case that this inquiry will be carried out by the HSE," the spokesman said.
It is now over three weeks since Savita (31) died in Galway University Hospital following a miscarriage on October 28.
Her husband Praveen says that in the days before she died, she had requested a termination after she was told she was going to lose the baby.
However, he claimed she was denied this as a foetal heart rate was still being detected.
Despite the three Galway staff stepping down from the inquiry team, her devastated husband Praveen believes the investigation would still be biased.
"It doesn't matter who sits on this panel. It's a HSE panel and I will not be cooperating with it," he said in an interview with the Herald.
"The only way to get to the truth is in a full independent public inquiry where evidence can be scrutinised. I have no faith in the HSE. Savita died in the care of the HSE.
"This is not just about Savita, this is about doing it for all the women of Ireland. This should never happen again."
The qualified engineer was speaking after spending a gruelling eight hours outlining Savita's final days in an interview with gardai. And Mr Halappanavar's lawyer today reiterated his client's call for a "full public inquiry".
"My client is just not happy with the HSE investigating its own actions. The HSE will be picking their own team and we have seen what that has done so far. We just couldn't possibly accept that there would be transparency," according to Gerard O'Donnell.
The head of the HSE team, London professor Sabaratnam Arulkumaran, has himself suggested that it is crucial he is able to meet Mr Halappanavar.
Fianna Fail Health spokesman Billy Kelleher today said it was "vital" that the minister makes every effort to get Mr Halappanavar on board.
"This family is devastated and going through a period of extreme grief. The whole process has been badly handled -- from the decision to remove the three Galway-based figures to the seemingly slow and lacklustre engagement with the Halappanavar family," he told the Herald.
Meanwhile, there were claims today that the head of the HSE inquiry, Prof Arulkumaran, is not suitable as he co-authored a report advocating abortion.