According to the BBC, the councils added that they would try to protect the most vulnerable once the welfare reform comes into force on 1st April.
The UK government has said it would provide councils with £150m to help those in need, but David O'Neill, of council governing body Cosla, was not satisfied with the reforms.
Mr O'Neill said: "Make no mistake here - no blame whatsoever can be put at the door of Scotland's councils for either introducing these measures or for the devastating impact that this legislation is about to have on our communities."
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He added that Cosla could "not stand idly by and allow local government's reputation and the credibility of individual councils to take the hit for this because these welfare changes are not of our doing".
The reforms include changes to housing benefit, that will result in council and housing association tenants having their benefits cut if they are deemed to have a spare bedroom.
Mr O'Neill did admit there was a need for some change to the current welfare system, but explained: "I am simply pointing out to those who will be hardest hit by these changes that it is not their local council to blame.
"Indeed, councils are going to be hit themselves with the double whammy of the massive increase in people seeking our help at a time of diminishing resources. The huge damage it will do to our communities is not something that Cosla can support, and nor should others.
"The UK Government is transferring cost and responsibility for the needs of people on benefit on to local government."
(JP)
