WordNet sense 1 (a defense of some offensive behavior or some failure to keep a promise etc.):

alibi, exculpation, self-justification

WordNet sense 2 (a poor example):

apology

WordNet sense 3 (accept an excuse for):

pardon

WordNet sense 4 (defend, explain, clear away, or make excuses for by reasoning):

apologize, justify, rationalize, apologise, rationalise

WordNet sense 5 (ask for permission to be released from an engagement):

beg off

WordNet sense 6 (grant exemption or release to):

exempt, relieve, let off

WordNet sense 7 (serve as a reason or cause or justification of):

explain

WordNet sense 8 (excuse, overlook, or make allowances for; be lenient with):

condone