• Walkers make their way along Colinton Road. Picture: Jayne Emsley
The Scottish Government has been asked to sanction the secondment of troops to the city to help with relieving residential areas worst affected by the snowfall.
Army chiefs at Redford Barracks have also been in discussions with the council over the emergency plans to bring in the military manpower.
Up to 30 inches of snow have fallen in parts of the Capital since the cold snap hit last week. But Labour councillor Andrew Burns today said the clarion call to the British Army could be a case of too little, too late for Edinburgh's winter wonderland.
He said: "I very much welcome this, but (Labour] have been pressing very hard behind the scenes for this.
"It's too late now in some respects for this action and should have been done earlier, perhaps at the back end of last week when it was obvious to everyone there was a serious problem.
"The administration need to reflect on whether they could have done this earlier."
More: The big freeze
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• How you are affected
• The big freeze: your say
The council claims to have brought in more contractors than any other local authority in Scotland to combat the exceptional snowfalls and has deployed 30 gritters round the clock to clear main roads and arterial routes in the city.
Despite constant gritting, ploughing and other snow-clearing work, fresh heavy snowfall on Monday has hampered their efforts in the previous week, they say.
Lib Dem councillor Robert Aldridge, the city's environment leader, said the Army could provide valuable assistance but warned a deal had not yet been concluded.
He said: "The people of Edinburgh would expect us to do everything to remove the snow from residential streets as quickly as possible, while we continue the vital work of keeping the city's main thoroughfares open.
"It is not a done deal, but we have to look seriously at this option.
"If the Army is able to help it won't come cheap, but we believe it's a price worth paying to bring relief to our communities."
Meanwhile, Mark Turley, council director of services for communities, said: "We haven't concluded our discussions yet so none of the details have been firmed up, but I would hope we can move forward with this innovative plan in the next day or so.
"In submitting our request for assistance, I have stressed the extreme circumstances being faced by communities in the south and west of the city, and especially the urgency of ensuring that vulnerable people have access to health and care services."