Last week Stuart MacQuarrie, secretary of the Labour group on South Lanarkshire, complained that deputy council leader Edward McAvoy had used 'foul-mouthed and brutal verbal insults' against him.
The alleged incident took place at a private meeting just over a year ago, at which Mr McCabe was also present.
Scottish Labour Party general secretary Alex Rowley this week said he had interviewed all three councillors on Friday, two days after receiving the allegations.
'In particular, councillor Tom McCabe has been totally vindicated. Indeed, he should be commended for the way he has run the council.'
Mr Rowley also said Mr McAvoy 'regretted the upset' caused by the conversation.
The Labour Party said Mr MacQuarrie accepted the party's verdict that he had blown events out of proportion.