Lines company Orion says 6,000 properties in Canterbury's Selwyn District are still without power and it's likely that hundreds will still be cut off on Monday. It reconnected 500 more on Friday.
The areas without power are predominantly in the rural region west of Christchurch, with smaller areas within Christchurch city also affected.
Orion chief executive Rob Jamieson says the priority is to reconnect the areas with the most customers first
In North Canterbury, Main Power restored power to about 1,000 customers on Friday, leaving 1,500 still without power.
Main Power is confident that only those in isolated areas may remain without power by Monday.
In the North Island, Powerco says 150 customers still have no power in Taranaki, Wairarapa, Tararua and Manawatu.
Tens of thousands of customers were blacked out during the storm that hit most of New Zealand from Tuesday.
Mr Jamieson says all available crews are trying to restore power to a severely damaged rural substation in Burnham, which cut power to the Selwyn district.
"It is a very big event and the reason for that is that it is so widespread - so many trees and lines throughout the Selwyn district that it just makes it a very large job."
Mr Jamieson says neighbouring lines companies have not been able to help as they are fixing their own networks but contractors from Marlborough and Wellington are now assisting.
He says Orion is working with Selwyn District Council to prioritise water supplies.
The council says it is rotating diesel generators around water storage and pumping stations to reticulate water to properties as far south as Dunsandel and inland as far west as Sheffield and Springfield.
It is asking farmers to clear stock water races blocked by trees and debris, as it will take some time for contractors to get to them. Tankers are topping up in Darfield to supply water for stock.
The council is also directing people who need showers, and power points to charge phones and other electronic equipment, to motels, rugby clubs and community centres.