By Thursday, the low was expected to clear, however another weather system was expected to move in from the Tasman Sea, bringing rain to the west of the North Island, he said.
"As the low moves by the east, it is likely to bring with it some large swells for the North Island's eastern coastline, especially Gisborne, Hawke's Bay and Coromandel."
The South Island was forecast to enjoy a great start to the week, with a high pressure system bringing plenty of clear sky and sunshine for most through until Thursday, Mr Law said.
A weakening southerly would introduce colder air across the South Island by Friday, but the wettest weather would stay confined to the West Coast, he said.
The week ahead:
Whangarei:
* Showers, some heavy today, easing this afternoon. Strong southeasterlies also forecast. High of 16C, low of 11C.
* Rain or showers with strengthening westerlies forecast for Friday. High of 17C, low of 8C.
Auckland:
* Mainly fine today with fresh southeasterlies and isolated afternoon showers. High of 17C, low of 10C.
* Rain and strengthening westerlies forecast for Friday. Temperature drops to a high of 16C and a low of 8C.
Hamilton:
* Fine weather today with fresh southeasterlies easing this evening. High of 18C, low of 7C.
* Rain or showers forecast for Friday with westerlies picking up. High of 16C, low of 5C.
Wellington:
* Fine weather today with southeasterlies dying out. High of 15C, low of 5C.
* Rain or showers forecast for Friday with northerlies turning to cold southerlies at night. High of 14C, low of 6C.
Christchurch:
* Fine weather today with fresh northeasterlies. High of 14C, overnight low of -2C.
* Brief rain turning to showers with a cold southerly change forecast for Friday. High of 13C, overnight low of 1C.