It said the storms, expected to strike between 3pm and 10pm, would be accompanied by localised heavy rain and small hail. There was a low risk of small tornadoes.
MetService warned there was also a threat of intense downpours leading to flash flooding around low-lying areas such as streams, rivers or narrow valleys, along with slips.
It said driving would prove hazardous, with poor visibility in heavy rain.
Weatherwatch.co.nz said widespread rain was pushing ahead of the low, affecting eastern regions of the North Island including Bay of Plenty and Coromandel.
Parts of the North Island were expected to be deluged, with up to 100mm of rain falling in the Hawke's Bay region over the coming 36 hours, leading to the risk of localised flooding.
A heavy rain warning was in place for the Bay of Plenty east of Ōpōtiki and Gisborne north of Ruatoria, with rain expected to fall not only through the day but even more to come overnight.
The low wasn't classed as a storm, but the middle of the country would experience gale-force winds, with severe gales set to barrel through Cook Strait today, said the forecaster.
MetService said powerful southeast gales up to 120km/h were expected to hit Taranaki today and last through the night.
Gusty winds in excess of 70 km/h were expected to peak in coastal parts of Wellington later tonight and across much of tomorrow.
Scattered rain and snow was expected to fall in some eastern areas of the South Island today and overall temperatures were expected to dip markedly on the eastern side of both islands for the coming two days.
Snow was also expected to fall across the North Island above 1000m.
A road snowfall warning was issued for the Desert Rd with up to 2cm of snow expected to fall tomorrow.
South Island motorists were warned to expect up to 2cm of snow to fall overnight on the Lewis, Porters and Lindis Passes.
Weatherwatch.co.nz said another round of severe rain would kick in across the South Island on Sunday with heavy rain, snow and gusty winds likely in western coastal areas.
