On the Baltic Sea island of Gotland – home to almost 60,000 people – the disruption to phone lines meant that residents could not reach Sweden's emergency number 112.
Authorities instead urged Gotlanders to travel to their nearest fire station in the event of an emergency. Staff were called in to man the stations at Fårö, Fårösund, Slite, Dalhem, Kräklingbo, Visby, Klintehamn, Garda, Hemse and Burgsvik.
No emergencies were however reported overnight, Åsa Sköld at the fire and rescue services for Greater Stockholm told the TT news agency on Thursday morning.
"We can't guarantee that it's possible to make calls, that's why the stations are manned. We don't know how many phones are not working, but not all of them are out," she said.
The official warning applies to noon on Thursday.
Electricity had been restored to most homes on Gotland by Thursday morning, although the phone network was still experiencing problems.
On the mainland, more than 36,000 households were still without power at 11am, including some 26,000 Vattenfall customers in Stockholm county and almost 4,000 in Uppsala.
In Norrtälje, fire stations were open for those who needed to charge mobile phones, get coffee, or take a break to warm up.
Homes in the Stockholm archipelago are expected to get power back by Thursday 6pm if they are close to the mainland. However, those living further out in the archipelago may have to wait until Friday, said Vattenfall, who has dispatched helicopters to transport backup power supplies to the islands.
Storm Alfrida, caused by low pressure air moving over from Iceland, led to major problems for transport in central Sweden on Wednesday, with fallen trees and scaffolding blocking roads and disruption to ferries.
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