It was also causing problems in Canterbury, with surface flooding reported in parts of Christchurch and Selwyn.
A flood alert is in place for the Halswell River and firefighters are helping to put up sand bags in Leeston, about 45 minutes southwest of Christchurch, where flooding is threatening homes.
A Fire Service southern communications spokeswoman said about 30 properties had reported surface flooding since 9am.
However, no houses had flooded yet and the sand bags were a precautionary measure.
In Wellington, the clean-up was continuing today in persistent heavy rain.
Civil Defence group chairwoman and Kapiti Mayor Jenny Rowan said hundreds of workers and volunteers had toiled in atrocious and often dangerous conditions to to get power restored, roads reopened, damaged roofs secured and fallen trees removed.
"However the clean-up is by no means complete - some areas are still without power. And with continuing rain there is potential for flooding," she said.
"We have reports that slips are still coming down in parts of the region and that there are trees and branches that could still come down. If in doubt, steer clear of storm-damaged trees and let the experts do the clean-up."
Ms Rowan urged residents to lend a helping hand to clear leaves and debris from drains, as council call centres were getting a steady stream of calls to report surface flooding.
Wellington City Council spokesman Clayton Anderson said the call centre has been dealing with a stream of requests all morning.
He said if homeowners think they are able to fix issues themselves, it would free up council workers to focus on more urgent jobs.
"If you are considering calling the council about a blocked drain outside your house, and you think that you could potentially deal with it yourself or you and a neighbour could deal with it yourselves, we'd ask you to get out there and muck in a bit.''
Most main roads around the region were now open, including the coastal road between Island Bay and Owhiro Bay, but motorists were advised to take care.
Council staff were today inspecting road access to the coastal community of Makara due to concerns the heavy rain may cause flooding in the area.
Wellington Electricity said a large number of the 30,000 customers who were left without power by the storm now had electricity restored.
However, about 1500 customers still have no power including in Whitemans Valley, Titahi Bay, Wainuiomata, Miramar, Kingsley Heights, Makara, Ohariu Valley, Newlands, Johnsonville, Plimmerton, Mana, Days Bay and Porirua.
A Wellington Electricity spokesman asked residents without power to get in touch.
"Significant progress has been made to restore service to as many customers' electricity service as possible on Friday and overnight Saturday, however the scale of the event means that these remaining customers are taking longer to restore."
Council welfare staff were organising help for some residents who were still without power.
In Canterbury, up to 5mm of rain was falling an hour in the Halswell catchment area, and the river was still rising.
Environment Canterbury said the river had reached almost 6.3m at 1pm - up to 2m above normal - which was a significant level for the river.
Anyone close to the river is advised to monitor their situation carefully.
Insurance Council chief executive Tim Grafton said it was too early to know just how expensive the damage in the Wellington area will be to repair, but claims were likely to run to tens of millions of dollars.
"A mixture of roof damage, windows blown in, and there could be water getting in as a result and damaging contents.
"Those are the likely things that would have come through.''
He said it would be a while before all the claims come in but it was already looking like a very expensive storm.
"We had severe flooding events in Nelson and the Bay of Plenty in April - that came to $36 million.
"This, we don't know, but it will definitely be running in the tens of millions.''
Mr Grafton said while people in other regions had also suffered damage, most claims would come from Wellington.
Meanwhile, the Interislander ferry Kaitaki, which slipped from its moorings in Wellington this week, needs further assessment before it can go back into service.
The Arahura will take its place in the meantime.
Further bad weather last night meant Interislander services were cancelled, but a KiwiRail spokeswoman said this morning the Arahura sailed with no problems.
"It left at 8.15AM this morning, and the Arahura at the moment is the only ship that is sailing. It's operating to the Kaitaki timetable.''
