AA Roadwatch says there are slippery conditions on roads nationwide, and that particular care is required on routes in east Leinster, Cavan, Mayo and east Munster.
Minister for the Environment John Gormley has said more heavy snowfalls are expected to make transport conditions deteriorate on Monday and Tuesday.
Speaking on RTÉ Radio, he said stocks of salt to treat the roads would have to be managed carefully and would be moved from one local authority to another to meet demand, as required.
Mr Gormley said local authorities had not run out of salt, but supplies were low, and had to be rationed.
Meanwhile, all flights into and out of Dublin Airport have resumed.
A decision was taken to suspend the flights shortly after 8.30am after two aircraft reported medium to poor braking action
Driving conditions remain hazardous following overnight freezing temperatures.
Motorists are again being warned to exercise extreme caution and avoid unnecessary journeys.
Roads are icy across the country as temperatures dipped to at least -12C in places.
With salt supplies running very low, local authorities have began using a mixture of sand and salt to treat roads.
The National Roads Authority has said it will be conserving stocks of grit over the weekend, to ensure that main roads can remain open next week.
Met Éireann says the severe weather could last for at least another week.
Dublin Bus says that subject to weather and road conditions it will be operating a full service on all corridors.
However, curtailments are in place in some areas, and passengers are advised to check the Dublin Bus website for updates.