PC Laura Sayer, 39, and PC Kenny MacKenzie, 43, were identified as the duo hurt while dealing with a call-out.
The two police officers were injured in the incident this morning at Gateside Gardens.
PC Sayer was still serving her probationary period and has been with the force for just six months.
PC MacKenzie has nine years’ service.
A Police Scotland statement said: “Both officers remain in a serious condition in hospital. We thank the public for all the good wishes received.
“Assistant Chief Constable Bernard Higgins has visited both officers in hospital today to express Police Scotland’s gratitude and support for them.”
A 43-year-old man had been arrested following an incident and is also being treated in hospital.
Police Scotland has referred the incident to the Police Investigations and Review Commissioner.
The Police Scotland officers, a man and a woman, were injured at a house on Gateside Gardens in Greenock this morning.
Colleagues praised the “incredible bravery” of the two injured officers, who were initially taken to Royal Inverclyde Hospital.
Police said the incident was not terror related and there was no risk to the wider public.
ACC Higgins has visited both officers and said he was “proud to speak to them”.
At a press conference in Greenock, he said: “Both remain in a serious condition.
“Our thoughts are with our injured colleagues and of course their families at this time.
“I’d like to take this opportunity to publicly praise the incredible bravery shown by these two officers during the extremely difficult and challenging situation they faced.”
One of the officers has been transferred to the Queen Elizabeth University Hospital in Glasgow for further treatment.
Asked about the nature of the injuries, Mr Higgins said: “It’s not been classified as life-threatening at this moment, but it is significant and it is serious.
“I went to the hospital and I spoke to both officers. They were in remarkable good spirits.
“I’m blown away by the courage of them. I was actually very moved and proud to speak with them.”
A large section of Gateside Gardens has been cordoned off and several police vehicles remain in the area.
A team of forensic officers could be seen examining a section of Grieve Road where a shoe and an item of clothing lay in the street.
Mr Higgins said the arrested man was being treated for “very minor bruising and cuts and grazes”.
He said the 43-year-old’s mental well-being was being assessed but stressed this was standard procedure for everyone who is arrested.
Police Scotland is to significantly increase the number of officers armed with tasers from this month.
Mr Higgins said: “Potentially a taser could have made a difference, but again that’s a bit speculative.
“Greenock is going to be one of the areas where during our roll-out period there will be specially-trained officers deployed.”
Andrea MacDonald, chair of the Scottish Police Federation, said: “Our thoughts are with the injured officers and their families. Once again we see how difficult and dangerous a job it is.
“Police officers put themselves between other professionals and the public and dangerous individuals, sometimes with life-changing consequences for themselves and their families. We wish our colleagues a speedy and full recovery.”
First Minister Nicola Sturgeon tweeted: “My thoughts and best wishes for a full recovery are with the two police officers injured on duty in Greenock today.
“This is a reminder of the vital but often dangerous job our police men and women do, and what a huge debt of gratitude we owe to them.”