The Transport Agency will consider extending a campaign advertising for the new giveway rules if it suspects motorists are not adjusting to the change.
The rules came into effect on Sunday morning and the police say the transition has gone smoothly, with very few reports of crashes or confusion.
But Transport Agency chief executive Geoff Dangerfield says the $1.2 million publicity campaign will be extended if required.
He says the advertising blitz is due to finish on Sunday, 1 April.
Vehicles turning right now give way to traffic from the opposite direction that is turning left.
Drivers at the bottom of T-intersections also have to give way to all traffic turning right from the other road.
Commuters appeared to have fared well with the new rules and police reported few crashes at intersections.
Nor had they phased most of the Auckland commuters Radio New Zealand spoke to on Monday morning.
Courier driver Juniah Filimoehala says he has not seen any problems during his rounds so far, while Mary Pickering says motorists have been well-behaved and the advertising and catchy jingles have helped her remember the rules.
Police say drivers are being cautious and courteous but the real challenge now will be for everyone to keep applying the new rules and not to slip back into old habits.
Geoff Dangerfield told Radio New Zealand's Morning Report the main difficulty will be changing habits so that the new rules become instinctive and expects that this could take quite a long time.
The Automobile Association says it will start teaching trainee drivers the new rules from Monday.
Campaign 'woefully inadequate'
A leading motoring commentator says the campaign to educate drivers has been woefully inadequate.
Clive Matthew-Wilson, of the car review website Dog and Lemon, says it is lucky there has not been chaos so far and a change of this magnitude requires more effort to make sure people are aware.
But Mr Dangerfield says all the evidence is that a short, sharp campaign is best.