More snow is forecast to fall tonight as icy conditions continue to hamper road users.
Renewed appeals have been issued to motorists for vigilance as hundreds of thousands of people returned to work after the Christmas and New Year break.
Snow and ice are making driving conditions hazardous on secondary roads across the country.
Primary routes have been gritted and are passable, although there is ice in places in some midland counties.
Snow has been falling throughout the day in parts of Leitrim, Longford and Donegal where road conditions have worsened.
The freezing temperatures are set to continue for the rest of the week.
Concern has been raised about diminishing supplies of salt and grit for treating roads.
Cavan County Council has said it will not be able to deal with any significant snowfall this week as its supplies are at a critically low level.
A senior engineer from Donegal County Council has said that county supplies are also worryingly low, but that the normal gritting programme for the county has been maintained so far.
In Dublin, local authorities say they have to concentrate on gritting main roads to maintain their stocks.
The National Roads Authority said the M50 has adequate supplies of grit.
Three ships are due into Cork Port this week each carrying 4,000 tonnes of salt to de-ice the country's roads. The first shipment of the salt, being imported from Torrevieja in Spain, arrived today.
Meanwhile, Dublin Bus says services on all routes are operating, although some have been curtailed.
Bus Éireann says the majority of its services are operating to schedule, with only some minor delays and changes to routes.
People travelling to and from Leinster are advised to contact their local office for information on individual services, as all routes remain under review.
AA Roadwatch says it experienced its busiest day ever with over 700 calls for assistance by lunchtime.
It says battery and electrical system failures were 'four or five times greater than a typical Monday'.
Met Éireann has said such a prolonged cold spell has not been seen in Ireland since 1963.
It confirmed that temperatures reached as low as -10C on Christmas Day.
The Simon Community, which works with homeless people, has renewed its appeal for donations as the cold spell continues.