The Health Information and Quality Authority has been asked by the HSE to consider starting a statutory inquiry into the death of Savita Halappanavar at Galway University Hospital last month.
However the HSE's own investigation is to continue.
The HSE's chief executive Tony O'Brien says Praveen Halappanavar's decision not to co-operate with its inquiry does not absolve the executive of its duty to investigate Savita's death.
He said it would be criminally negligent not to proceed with this investigation.
The HSE also says Praveen Halappanavar's consent is not required to allow Savita's medical records be examined by the investigating team.