Say it once, not over and over. Just go on record. If you’re wrong, say so; then change.
There isn’t much difference between the pathological apologizer and the pathological liar. The apologizer says sorry more often than a blinking yellow light blinks yellow. The liar won’t admit he was wrong, then tries to repair friendships with all smiles and no apologies.
Words and actions must go together. All words and no action doesn’t help anymore than all action and no words. We need both and we need them together in agreement. When wrong, say so once; then you’d better change.