Police commissioner Richard Chambers confirmed Ramsay was now in a stable condition, having been in hospital following being struck by a vehicle on New Year's Eve in Nelson.
Two members of the public that had been injured were also continuing to recover, he said.
Iwi from across Te Tau Ihu blessed the scene of the incident, in which a vehicle sped towards and collided with Fleming and Ramsay at about 2am, who had been patrolling Buxton Square on foot.
The vehicle then turned and drove at a police car, ramming it.
The 32-year-old driver of the vehicle was tasered and arrested at the scene, and is due to appear in Nelson District Court on Friday.
Fleming later died from her injuries.
Chambers said the attack was "unprovoked and senseless", and the driver would be charged with "serious criminal offences".
He said police had been heartened by the response from both the local community and further afield.
"I would like to thank Iwi for their support, along with members of the community who have delivered flowers, cards, and the thousands of messages we have received," he said in a statement.
"These have meant a lot to our staff in Nelson as well as to the wider police family.
"The coming days, weeks and months are going to be tough for the staff in Nelson, as they come to terms with what has happened. But it is an absolute priority for police that we wrap support around the staff directly impacted as well as the wider station.
"Additionally, a number of police forces across Australia, the Pacific, and Canada have reached out to New Zealand Police to offer their condolences."
He added they were supporting Fleming's family.
"We are doing everything we can for Lyn’s family, but this is an incredibly difficult time for them, as they come to terms with what has happened."
- APL with RNZ
