Chief Minister Michael Gunner has urged businesses that can stay closed to do so.
"Please look after yourself, your staff and families. If you don't need to open, don't open," Mr Gunner said on Sunday.
Marcus is expected to pass off the coast of far-north Western Australia after dumping more rain on the Kimberley region.
Wind gusts of up to 120 km/h are set to be confined to coastal parts between Mitchell Plateau and Cockatoo early on Monday before extending further south to Beagle Bay.
The Bureau of Meteorology predicts Marcus will move off the coast during the day where it is expected to intensify back into a severe tropical cyclone, however it is unlikely to move far enough south to impact Broome and Derby.
Heavy rain and flooding in low-lying areas is also likely to ease by the afternoon with drivers warned to check updates on road closures.
The highest rainfall was recorded at the Aboriginal community of Kalumburu which had more than 90mm of rain between 9am and 4pm on Sunday.
Tropical Cyclone Marcus is the fourth cyclone to hit the far north of WA this year, and the sixth to form this season.
Darwin felt the brunt of the tropical cyclone on Saturday, as 130 km/h winds brought down trees and power lines.
Emergency services moved quickly onto the clean-up with weather reports suggesting monsoonal activity could hit the region during the week.
NT Emergency Services Chief Officer Jason Collins has warned people to be careful cleaning up around their properties and to be wary of power lines.
"We cannot guarantee they will be made safe as yet. Most will be, but we cannot guarantee it at the moment," he said.
"If you see a line down or in an unusual position, treat it as live."
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