Arrest warrants have now been issued for those responsible for the hit-and-run in the Knightswood area of Glasgow on Sunday night.
While both officers are now recovering, there had initially been concerns for the female officer after she was admitted to intensive care.
Appearing before the Scottish Police Authority (SPA), Deputy Chief Constable Iain Livingstone said we was satisfied the inquiry had been “well resourced” and the tactics used “appropriate”.
It followed criticism from the Scottish Police Federation earlier this week that the force had waited too long to issue a public appeal through social media.
Mr Livingstone said the female officer might have died had it not been for the actions of her colleague.
He said: “Thankfully, our colleague is now out of intensive care and the condition of both officers is improving. A full, thorough and proper investigative response was put in place and next of kin notified.
“A public appeal for information was made as part of the ongoing investigation. Inevitably, the incident received a significant amount of media attention and rightly so. A Scottish Police Federation representative was briefed in Glasgow by the local superintendent at 8.30am on Monday.
“An incident such as this which results in police officers receiving serious injuries while carrying out their duty, reverberates around the organisation.
“I’m satisfied that the investigation is well resourced and the tactics utilised by the investigators, including media engagement, are appropriate.
The actions of investigators are consistent with recent similar inquiries where members of the public were the victims. At this time, I can assure members of the SPA and the wider public that the provision of accurate information in the public domain was timely and in no way compromised public safety.”
Mr Livingstone also made reference to the recent convictions of those responsible for the murders of Surjit Singh Chhokar and Paige Doherty as well statistics showing the number of homicides at its lowest level in Scotland since 1976.
He said: “One of the great virtues of bringing the police services of Scotland together as one was to allow the recourse to specialist support. Thankfully, homicides are atypical incidents that don’t happen on a regular basis.
"What we’ve been able to do with the creation of Police Scotland is create Major Investigation Teams (MITs) and their prime function and role is to investigate murders and suspicious deaths. We can now bring a high quality and standardised approach to every investigation. Our departments before were filled with very skilled officers, but our structures were not fit for purpose.”