As of 8pm on Monday evening, energy company SSEN said power was restored to 100,000 customers with around 16,900 customers remaining off supply
The Met Office yellow weather warning of wind is in place until 6pm on Tuesday.
The main areas which continue to be affected are rural Aberdeenshire and the Angus border, with some customers also off supply in Perthshire, the Highlands, Western Isles and the Moray Coast.
With support from over 400 additional engineers and support staff, SSEN said they aim to reduce the number of customers off supply to around 7,000 overnight.
Restoration efforts will continue into Tuesday with the possibility that for small clusters of customers affected by Storm Corrie, this may extend into Wednesday.
SSEN has deployed welfare facilities to locations across Scotland and hot food and drinks will be served from 9am on Tuesday.
Customers unable to access welfare facilities and who remain off supply may claim back the cost of meals up to £15 per person.
Richard Gough, Director of Distribution System Operations at SSEN, said: “Our teams have continued to make strong progress restoring power to customers impacted by the extreme weather from Storm Malik, with over 92% of those customers restored.
“Whilst our teams are making every effort to restore customers as soon as possible, the cumulative impact of Storms Malik and Corrie has compounded the restoration challenge. As a result, we are advising customers that while expected restoration of customer supplies from Storm Malik remains Tuesday evening, restoration times for some of those impacted by Storm Corrie may now extend to Wednesday.
“We would like to apologise to all customers affected and would like to reassure them that all available resources have been deployed to support with restoration efforts and our teams are doing all they can to safely restore power as quickly as possible.
“We continue to proactively contact customers on our Priority Services Register to offer extra support where required and work with local resilience partners to coordinate welfare provisions. I’d encourage any customer concerned to give our dedicated teams a call on 105, where we can provide additional support and guidance.”
First Minister Nicola Sturgeon has chaired a further meeting of the Scottish Government’s Resilience Room (SGoRR) to co-ordinate the response to Storm Malik and Storm Corrie.
A yellow warning is still in place covering Lewis, the Orkney Islands, much of the Highlands, Grampian and Tayside areas.
Deputy First Minister John Swinney said: “The power companies have drafted in a large number of additional engineers and are making significant inroads into reconnecting customers, with work continuing at pace this evening.
“I want to thank all those who are working in difficult conditions to keep people safe and maintain our lifeline services.
“For those who will unfortunately not have power tonight, support with alternative accommodation is available to anyone who needs it. Those who have found their own accommodation can seek reimbursement from their suppliers. Special arrangements remain in place for vulnerable customers and local resilience partnerships continue to work together to provide welfare support.”
Anyone without power who needs advice or support can call an assistance phone line on 0808 196 3384.