Power company Eon sent 1,500 of its workers into forests hit by the strom to begin work repairing cables.
Meteorological agency SMHI is forecasting more strong winds in mountainous areas and at sea. But the worst of the storm, labelled Per by Norwegian meteorologists, is now deemed to be over.
Only 50,000 of the households that suffered power cuts in the storm had got their electricity supply back by Monday morning.
“This is really severe. We are very, very distressed,” said Eon’s spokesman Mattias Hennius.
Of the power companies affected by the storms, Eon has been hit hardest.
At 6 a.m. on Monday the company sent 1,500 workers and around a hundred vehicles into the forests affected by the storm to clear trees and repair damaged cables. Eight helicopters have been sent out to locate the affected areas.
The southern half of the country, primarily Skåne, Västra Götaland and Svealand, bore the brunt of the storm. It is not yet certain when customers in these regions will get their power back.
“But it will take quite a few days before everybody has electricity again,” said Hennius.
By Monday morning the storm had finally dissipated in most of the country.
On Sunday rail traffic came to a practical standstill but now trains are running again between Stockholm and Gothenburg.
“But passengers can expect delays,” said Susanne Alemyr, spokeswoman for Banverket, the company that control’s Sweden’s rail network.
Trains have also begun running again on the Gothenburg to Malmö route, though with significant delays.
All trains in the Småland and Blekinge regions have been cancelled until further notice.
Although many rail routes out of Gothenburg have not yet resumed service, public transport in the city is back on track, as are air and ferry services.
A number of schools and pre-schools in Kronoberg County will remain closed on Monday as a result of destruction caused by the storm, Sveriges Radio reports.
Three people died as a result of hurricane winds that battered southern Sweden on Sunday.
One man in his 60s died when the car he was travelling in was hit by a falling tree near Forserum, said police in Jönköping county. A woman who was travelling with him was slightly injured in the accident, which happened at around 1pm.
In Motala a nine year old boy died after a tree fell on him at around midday. The boy was taken to hospital where he was pronounced dead.
During the afternoon a man aged 25 was badly injured when the light van he was driving on a road near Ullared in Halland was hit by a falling tree. The man, who was alone in the truck, died later in hospital in Varberg.
The storm hit Sweden from the west on Sunday morning. On Hanö, an island off the coast of Blekinge, the wind speed reached a peak of 40 metres per second, or 144 kilometres per hour, at around 2pm.
“That’s very unusual in Sweden. I don’t think we’ve had such high figures since ‘Gudrun’ in January 2005,” said meteorologist Jonas Höglund at the Swedish Meteorological and Hydrological Institute (SMHI).
On the west coast a top wind speed of 39m/s was measured on Måseskär, outside Orust. However, the storm had started to weaken there by 2pm.
In eastern Sweden the storm reach its peak on Sunday evening.