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The Bureau of Meteorology on Saturday morning downgraded Ita to a category two cyclone - from a category four when it hit the coast - as it tracks south across the state.
At 6am (AEST) the cyclone was 20km southwest of Cooktown and 160km north of Cairns and moving at 8km/h, BoM said.
The forecaster said a cyclone warning was current for coastal areas from Cape Melville to Cardwell including Cooktown, Port Douglas and Cairns, and extending inland to areas including Mareeba and Chillagoe.
BoM said destructive winds of up to 130km/h were possible between Cape Tribulation and Port Douglas "for a brief period this morning".
Gales with wind gusts of up to 110 km/h were possible between Cape Melville and Port Douglas, as well as in areas including Mareeba later today, and as far south as Innisfail, Chillagoe and Cardwell this evening.
BoM warned coastal residents between Cooktown and Cairns, including Port Douglas, of a storm tide this morning, and said heavy rain could lead to flash flooding in parts of the Peninsula, North Tropical Coast and Tablelands districts.
Daryl Camp from Emergency Management Queensland says emergency crews were assessing the damage in Cooktown.
"We're hoping to be able to do that fairly quickly this morning, we've got two crews doing rapid damage assessment and two crews doing cleanup and trying to see if anybody needs assistance," Mr Camp told ABC Radio.
He said it would be safe for people to leave their houses and shelters when the winds died down about 9am or 10am.
"But we'll have to wait and see what Ita has done," he added.
Ita crossed the coast near Cape Flattery, with winds near the centre up to 230km/h, about 10pm on Friday.
By midnight, Ita had been downgraded to category three with winds gusts up to 117km/h had recorded in Cooktown just after midnight.
At least one roof was torn from a house in Cooktown, which was battered by strong gales and heavy rain.