However, by the weekend temperatures should have risen slightly thanks to a new weather system blowing in.
"We're going to find things change a little bit as we head through the next few days. We get a bit more cloud, a bit more of a breeze," Mr Law said.
"We've still got some cold nights to come but hopefully we're going to see the back of these incredibly cold nights."
Winds blowing in from the southwest would bring warmer nights and some rain this weekend, Mr Law said.
Over the weekend, Auckland could expect southwesterly winds with some showers to come.
"It's not nearly as cold during the weekend ... but I think we are going to find from Friday onwards some showers and a bit of early rain first thing on Saturday morning.
"The good news is with a bit more cloud and a bit more breeze, our temperatures overnight won't drop down nearly as cold."
But before the weekend, temperatures were expected to stay low.
"If we've got those cold temperatures overnight, those daytime temperatures are a struggle to get any higher," Mr Law said.
Central parts of the South Island, particularly Central Otago and Canterbury, could expect temperatures around -20C again tonight, he said.
Further north, things would stay relatively chilly as well.
"The North Island -- another cold one to come," Mr Law said.
When asked if he thought temperatures would drop even lower in the coming nights, Mr Law said it was a possibility.
"It's not out of the question at all, but I think what we're going to see is temperatures that are very similar," he said.
"I think we are going to find it's still an incredibly cold night ... particularly in that central part of the South Island where you'll find temperatures similar to what we've seen the last few nights."
Tuesday night coldest recorded temperatures around the country:
Auckland (Whenuapai) -2.1C between 7am and 8am
Hamilton (airport) -1.1C between 3am and 4am
Tauranga (airport) 3.3C between 6am and 7am
Wellington (Kelburn) 5.7C between 11pm and midnight
Christchurch (airport) -3.6C between 5am to 6am
Dunedin (city) -0.7C at 6am and (airport) -6.9C between 8am and 9am
In the North Island, the coldest spot was Taumaranui with -4.9C about 7am
In the South Island, the coldest spot was Tara Hills near Omarama with -21.0C at 8.30am
(Source: MetService)
Weather for the weekend for the main cities:
Auckland -- Rain expected on both Saturday and Sunday and southwesterlies blowing through. A high of 15C for both days. An overnight low of 11C expected for Saturday and 12C for Sunday.
Hamilton-- Showers and westerlies will hit Hamilton over the weekend. While Saturday will be slightly sunnier, Sunday will be warmer, with highs of 14C and 15C respectively and lows of 7C and 8C.
Tauranga -- After some early showers on Saturday the weather should be fine for the rest of the weekend, with some winds. Saturday has a high of 15C and a low of 8C and Sunday has a high of 16C and a low of 9C.
Wellington -- Showers clearing by the end of Saturday as northwesterly winds develop. Saturday high of 13C and low of 8C, Sunday high of 14C and low of 8C predicted.
Chistchurch -- Weather will be fine but cold in Christchurch this weekend. A high of 11C is predicted for Saturday and the overnight low is expected to dropped below zero again to -1C. Sunday is slightly warmer with a high of 13C and a low of 1C predicted.
Dunedin -- Showers on Saturday clear by the end of the day before returning late on Sunday. A high of 11C and a low of 5C predicted for both days.
(Source: MetService)
