As many as 17,000 evacuees are seeking shelter in Louisiana and Texas hotels.
At least 14 deaths in Louisiana have been attributed to Hurricane Laura.
Four deaths in Texas were connected to the storm.
With over 350,000 still without power, officials said outages could last for weeks.
Schools in Calcasieu and in Cameron parishes will remain closed until further notice.
Nearly 308,000 Louisiana homes and businesses remained without power on Monday morning, according to poweroutage.us. Texas had more than 57,700 customers without electricity.
About 500 electricity transmission towers are down in the Lake Charles area alone, Edwards said.
More than 17,000 linemen from at least 29 states are making repairs, the governor said.
Customers have been warned it could be four or five weeks — if not longer — before their electricity is restored.
More than 180,000 people also have little or no running water. At least 183 water systems remain shut down after being slammed by Laura.
Close to 9,000 people are sheltering in hotels throughout the state. As many as 8,000 are in Texas hotels.
Death Toll Climbs to 18
The Louisiana Department of Health announced two more deaths Sunday as a result of Hurricane Laura, bringing the total in the state to 14. Of the 14 deaths, eight were due to carbon monoxide poisoning.
These are the confirmed victims in Louisiana:
-14-year-old girl, Vernon Parish, fallen tree
-51-year-old man, Jackson Parish, fallen tree
-68-year-old man, Acadia Parish, fallen tree
-64-year-old woman, Allen Parish, fallen tree
-Man, Calcasieu Parish, drowning
-24-year-old man, Calcasieu Parish, carbon monoxide poisoning from generator
-56-year-old woman, Calcasieu Parish, carbon monoxide poisoning from generator
-61-year-old man, Calcasieu Parish, carbon monoxide poisoning from generator
-81-year-old woman, Calcasieu Parish, carbon monoxide poisoning from generator
-72-year-old man, Calcasieu Parish, carbon monoxide poisoning from generator
-84-year-old man, Allen Parish, carbon monoxide poisoning from generator
-80-year-old woman, Allen Parish, carbon monoxide poisoning from generator
-57-year-old man, Calcasieu Parish, head injury after falling from roof
-One resident, Calcasieu Parish, carbon monoxide poisoning
In Texas, three men died in Port Arthur because of carbon monoxide poisoning from a generator they had brought indoors while sheltering from Laura, Jefferson County Precinct 7 Justice of the Peace Brad Burnett told KBMT-TV.
A 54-year-old man was killed Thursday when a tree fell on his mobile home, Sabine County Emergency Management Coordinator Kerwin Lloyd said, according to the AP.