"We must continue to fight. I have promised her family," he said.
"They are still waiting for the truth. I just talked to her father and he is concerned as to why it is taking so long to start the investigation; it has almost been a month. They are very concerned," he said.
Mr Halappanavar yesterday met Health Minister James Reilly. During the 30-minute private meeting he expressed both his own concerns and those of Savita's family.
He thanked the minister for expressing his condolences.
"It is [important] for the family because there is no comment or officials who called us or met us to pass on their condolences," he said.
Mr Halappanavar says the support he has received from Ireland and around the world has helped him continue with his campaign.
"It has been overwhelming. We never thought we would have such support," he said.
Gerard O'Donnell, Mr Halappanavar's solicitor, said he hoped the minister would now establish a public inquiry into Savita's death.
Mr O'Donnell said no timeframe had been set down for the minister to reply to Mr Halappanavar's concerns.
"I think he wanted to digest what I had to say and we ourselves at the same time, notwithstanding what the minister is going to do, have to continue to forge on and decide whether or not it will become necessary to go further with this from a legal perspective in terms of bringing any application to the European Court of Human Rights," he said.
Dr Reilly declined to rule out a public inquiry into the matter.
"The first thing we have to do is get this investigation completed and that will happen over the next number of week. At that point in time, further actions may be necessary."