Caerphilly County Borough Council has vowed to clear the waste and recycling backlog by Monday.
The local authority is telling residents to leave any uncollected waste or recycling out for collection.
However the council has admitted that there may still be some side streets where access could still be a problem for dust carts and the sheer amount of waste that needs collecting might also slow down the catch-up process.
Councillor Lyn Ackerman, cabinet member for the environment, said: “Like many other councils across the country our waste collection service has been severely disrupted by the recent bad weather.
“The safety of the public and our collection crews is paramount and we have needed to suspend many collection rounds over recent weeks due to the danger caused by the snow and ice.
“We hope to catch up over the weekend and in the early part of next week and will resume normal service as soon as conditions allow. Hopefully local residents can appreciate the difficulties we are facing and we would like to thank everyone for their patience and understanding.”