Winds blowing at a speed of up to 60 kilometres (38 miles) an hour reduced visibility to less than 300 metres (yards) at Kuwait airport and less than 150 meters at ports.
"We have halted oil exports until weather conditions improve," Kuwait National Petroleum Co (KNPC) spokesman Mohammad al-Ajmi told AFP, although operations at Kuwait's three oil refineries were not affected.
Issam al-Zamel, head of operations at the civil aviation authority, told the KUNA news agency that incoming planes were facing difficulty landing.
A flight for Kuwait's Al-Jazeera private airlines from Dubai was diverted to Bahrain, he said.
Scheduled flights out of Kuwait were still taking off by early afternoon.
The meteorological department was forecasting the dust storm would continue until Wednesday.
Kuwait has had virtually no rain for the third winter in a row, making desert sand loose and easily carried by strong northwesterly winds.
Author: Ksenia Kochneva
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Dust Storm Halts Oil Exports from Kuwait
A blinding dust storm hit Kuwait on Tuesday, halting oil exports and forcing the closure of the Gulf emirate's three ports besides disrupting air traffic, AFP reported