Traffic at airports in Benghazi and Tobruk was suspended until further notice, local media said, showing images of runways buried in sand.
"All flights to and from the Benina International Airport (in Benghazi) have been postponed due to poor visibility and poor weather conditions," Saleh al-Amrouni, the airport's manager, told al-Masar TV channel.
Authorities in the east announced as early as Sunday that Monday and Tuesday would be "public holidays" owing "to bad weather conditions," national press agency Lana News reported.
Among the areas where a state of alert has been declared is Derna, where more than 4,300 people died and over 8,000 disappeared last September when a gigantic flood swept through the city following the collapse of two dams.
Libya is still struggling to recover from years of war and instability after the 2011 overthrow of longtime dictator Moamer Kadhafi.
The hydrocarbon-rich country is divided between the UN-recognised Tripoli-based government in the west and a rival administration in the country's east.
Authorities have also called on law enforcement to limit road traffic and movement in areas where the sandstorm has caused poor visibility.
In Tobruk, Al Bayda and Ajdabiya people were reportedly forced to stay at home as the skies turned yellow.
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