"We've also got excellent support from local iwi and LandSAR volunteers with the search operation."
Inspector Taylor said it was understood the group were equipped with warm clothing, but it was unclear how much food they had given they were on a short walk.
The weather in the area was fine, still and reasonably warm.
"Our hope is that they have been able to shelter somewhere and keep warm until we can get to them.
"With young children in the group, there are obvious concerns about their welfare, but we have experienced search teams working their way methodically through the search area and our hope is that they will be found safe and well."
Taylor said the search would continue throughout the day and re-assessed as any new information came in.
Police launched an extensive search and rescue operation after the group were reported overdue yesterday from a walk in the Otamatuna Ridge area, North East of Murapara.
They had been dropped off at the Otamatuna Track on Tuesday afternoon for a two hour walk.
The group spent a night in the wilderness before the alarm was raised at 4pm the next day.
The woman who took the children into the bush is from the area.
Helicopters and searchers have been scouring a number of tracks on the dense and difficult terrain since yesterday evening.
Today searchers were focusing on a number of tracks around Lions Hut.
Most of these tracks involve steep climbs up challenging terrain.
According to the Department of Conservation website only the Te Waiiti Stream via Te Pona a Pita track is suitable for less fit walkers and suitable for all ages.
It is a two-hour walk and starts with a graded climb around the side of a ridge.
Conditions last night were dry for the youngsters who had spent their second night out in the open.
MetService forecaster said last night temperatures dropped to single digits but it was fine and there should not have been too much wind.
"Temperatures may have dropped to 3C, but it was not an exceptionally cold night. It certainly wouldn't have been pleasant, though passing cloud would have kept temperatures warmer. No rain was recorded in the area last night," he said.
Mountain Safety Council chief executive Mike Daisley said it was unfortunate this was the third incident in recent weeks where people had needed rescuing after unintentionally spending nights out in the bush.
He said if adults were taking children into the bush they needed to realise any outing would be slow-going.
"If you are taking children recognise that they are going to take a lot longer. A two hour walk could end up a day long tramp."
He said it was vital people take a windbreaker and nourishment on any outing into the bush, even if the weather forecast was good.
A spokesman for local iwi Tuhoe said concerns were mounting for the group, especially as the woman may not have taken a large amount of food on a short bush walk.
Local Tuhoe with expert knowledge of the area had now joined the search effort for the missing group.
"We're assisting by providing local information when the headquarters team requires that," said Ngai Tuhoe operations development manager Glenn Mitchell.
Mr Mitchell said it was unlikely the woman, aged in her 40s, had managed to reach any of the ridge-top huts however everyone was in suitable clothing for the outdoors.
"I understand they had warm clothes on," he said.
Mr Mitchell said the youngest children were just 4 and 5 years old.
He hoped given their age would mean they would not be able to travel far into the rugged Waimana Valley.
The missing woman has been described on social media as a very experienced bushman who knew the forest well.
Te Urewera contains the largest forested wilderness remaining in the North Island.
It is famous for its lakes and forests, its remote and rugged terrain and popular walk around Lake Waikaremoana.
The area is a favourite with hikers, kayakers, hunters and fly-fishing enthusiasts.
Anyone who has seen the group is asked to contact Bay of Plenty Police on (07) 348-0099.
