The country's second largest electricity retailer Powerco hopes to have electricity supplies back to full service by the end of the day.
About 340 Powerco customers in the Tauranga, Thames Valley and Coromandel areas remain without power as a result of the storm that struck on Thursday evening.
The storm initally left about 9000 customers without electricity, but Powerco Network Operations Manager Phil Marsh said staff were working hard to get supplies fully restored.
"Multiple crews were out in the field at first light to continue to the job of restoring supply to the final pockets of customers and we hope to have our high voltage supply restored by the end of today.
"But we know from experience there could be damage to customers' own service lines we are unaware of. These are the lines that go in to a property from the roadside. If people see their neighbours have power and they don't, they must contact their retailer who will report it to Powerco."
He said power could be temporarily turned off again near Thames as staff worked along roading contractors on the severely damaged Thames Coast Highway.
"We may have to take the power off for safety reasons as the roading contractors clear slips and complete other tasks near our network."
Mr Marsh said people should still take extreme care around fallen power lines and keep at least 4 metres away.
Downed lines should be reported to emergency services or Powerco immediately.
Earlier, a severe weather watch was issued in Bay of Plenty, with possible rainfall of 30 to 50 millimetres before 11am.
MetService meteorologist Tom Bell said there was some uncertainty as to the exact location of the heavy rainfall but it could add to the issues those areas were already having as the cleanup from the storm continued.
Mr Bell said other parts of the country would also get showers this morning. However, they are not expected to cause any problems.
The forecast says a trough of low pressure moves slowly northwest over the western Bay of Plenty and southern Coromandel peninsula this morning, bringing a risk of brief heavy rain.
The risk of heavy rain for the Coromandel has been lifted, but some heavy falls are still possible in the Bay of Plenty, a MetService update said.
The New Year storm brought heavy rains and strong winds, with one woman killed in Rotorua after a large oak tree came down on her vehicle, while most of the Coromandel Peninsula was hit by flooding and numerous road closures.
A massive clean up of the storm damage started in earnest on the Coromandel peninsula yesterday and along the coast in the Firth of Thames.
The Thames Coromandel District Council this morning said about 70 properties around Thames and about 30 at Opito were still without power but connections were expected to be reinstated by mid-morning.
"The Thames Coast Rd (SH25) from Tararu (immediately north of Thames) and Manaia is still closed, In order to help establish access to coastal communities, NZ Transport Agency contractors have set up a pilot vehicle convoy for residents only which will run from Tararu through to Te Puru. Through traffic will not be permitted, so please don't come for a look if you are not a resident."
The council said it may be some time before the road opens to the public.
The Half Moon Bay ferry terminal in East Auckland remains closed after the wharf was damaged by Friday's storm.
Auckland Transport says ferry services have been cancelled until further notice.
The damage will be assessed tomorrow.
People who travel to the city from the terminal are advised to find alternative transport options.