The call comes from the Welsh Local Government Association, which is supporting a campaign to have the charges brought against the soldiers erased from the record books.
The case centres of the view that the men were suffering from what is now recognised as post traumatic stress disorder.
The government recently turned down an appeal for the men to be pardoned despite evidence that many of those executed were not only very young but had experienced sustained bombing and machine gunning.
The association wants chief executives of councils to write backing their councillors' wishes that the pardons be issued to mark the end of the 20th century. The campaign, led by Wear Valley DC, has the support of the Royal British Legion.