Use 'intercede' when someone actively works to settle a disagreement or fight. A neutral friend can intercede to mend the rift between them.
Pro Tip 2/3
Neutral Position
The person who intercedes usually doesn't take sides in the dispute they are mediating. The counselor interceded without favoring either party in the conflict.
Pro Tip 3/3
Voluntary Action
'Intercede' suggests a voluntary action to help resolve others' issues. He wasn't asked but chose to intercede in the heated debate.