AA spokesman Conor Faughnan has predicted that tomorrow will be the busiest day of the year for his organisation as it faces thousands of call-outs to assist motorists whose car batteries will fail.

"Extremely cold weather affects car batteries and they are more likely to let you down", he said. Most people return to work after Christmas on Monday and a lot of people will not have moved their cars since the start of the holiday so we advise anyone returning to work tomorrow to start their car today and leave it run for a while."

Faughnan's warning comes amid widespread anger about the response of local authorities and the National Roads Authority (NRA) in gritting the country's icy road network.

The NRA – which has responsibility for the country's motorways – has expressed concern that supplies of rock salt road grit are running very low in some areas. Fine Gael TD Denis Naughten has asked the government to get the Emergency Planning Office to coordinate the response to the cold snap.

"The lack of any centralised planning has seen local authorities run out of salt and grit," he said. "The roads are not being gritted to the extent they should be. Councils have used about two months' supply of rock salt in the last 12 days so there is a huge crisis."

A spokesman for transport minister Noel Dempsey said: "Money was made available at the start of the year to every local authority and it was made quite clear that money was to be set aside for the gritting and salting of roads... We totally refute Denis Naughten's claims."

Faughnan said: "We got complaints about main roads not being gritted on Christmas Eve but to be fair to the local authorities the gritting has done been pretty well.

"There is no possibility for any local authority to get the entire road network gritted. We have 90,000 kilometres of secondary road so we have a huge amount of road given our sparse population. Gritting is not a magic wand especially when temperatures are dropping to -10°C."

Pat Clarke of Met Eireann warned: "It is going to stay cold for the next week with no sign of a change in this cold regime.

"It is going to remain very frosty and icy at night with temperatures dropping to 5°C to -9°C at times, with ground temperatures of -10°C or -11°C on the grass."

"Temperatures are going to struggle to get into low positive figures of 4°C or 5°C during the day. The other complication is that we may have scattered wintry showers of hail, sleet or snow as there will be no let up in this cold snap."