It has been issued from noon on Tuesday until noon tomorrow.
The Met Office cautioned that roads and railways may be affected.
There is also an increased risk of road accidents and falls on icy pavements.
The PSNI said 19 reports of traffic accidents have been reported since 5pm on Monday in Derry City and Strabane area.
A number of primary schools across Co Derry were closed today because of snow and icy conditions.These include Long Tower, St Patrick’s Pennyburn and St Brigid’s.
Translink bus services was also hit with delays and disruption in the area.
Speaking to BBC Radio Foyle, Mr Durkan said his office was inundated with calls for assistance and that the Department for Infrastructure (DfI) had “come up short”.
“It’s awful that schools are having to close because of the state of the roads around the district, it’s shambolic to be frank.
“There was chaos around the city last night, we were inundated with calls, photos and video footage of collisions.
“We do our best to relay these requests to DfI. In some instances I was able to assist personally on different streets with salt, but the bigger picture is that DfI have come up short here.”
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