"It's all about ensuring people travel at safe speeds to get through their journey safely rather than issuing tickets."
Smooth traffic flow was a priority, in part because a crash in the tunnel would mean major disruption and traffic delays.
McKennie said police were continuing monitoring in and around the tunnel as people got used to the new route.
"Various monitoring of traffic flows and driver behaviour to date has been really encouraging, with average traffic speeds coming in below the 80km/h speed limit set for the tunnel," he said.
"That's something we very much want to continue, so we will be continuing to work closely with the Transport Agency to ensure the safety of everyone using the tunnel.
"While our preference would be not to issue any notices, the 80km/h speed limit is in place for good reason to keep everyone safe, so we won't hesitate to prosecute where appropriate those who ignore the limit and put others on the road, and themselves, at risk."
Police retain none of the fines from speed cameras. This goes to the Government's consolidated fund.