There could also be some rain by the end of the week, Mr Law said.
"But generally, high pressure should dominate most of the week."
It could still be fairly cold in the south, and fog will be quite slow to clear during the day in places like Alexandra and Queenstown, he said.
It was too early to say whether the country could be disrupted by fog, similar to that seen last week.
"As we go through the week and lose the high pressure, the winds will pick up and that will help mix the atmosphere and we should find those fogs disappear."
Meanwhile, Niwa has just released its climate outlook for the next three months, which predicts a drier late winter.
Seasonal rainfall totals are expected to be below normal in areas of the east, including Hawke's Bay, Gisborne and the Wairarapa.
Combined with expected normal temperatures, this means people may start heading to the eastern beaches earlier than usual, said Niwa senior climate scientist Dr Brett Mullan.
"Late winter is still a bit early to see swimmers, but the prospect of drier weather on the way will be welcome news for many," he said.
Dr Mullan expected the worst of the unusually heavy rain, that caused chaos around the country last week, was over.