Merci pour l'invitation, mais je ne pourrai pas venir.
to send an invitation is 'envoyer une invitation' in French.
l'invitation
Say thankyou for the invite, but then say that you don't really feel like attending.
refuse his invitation
They tend to tell a white lie and say that they have something else on at the date or time.
Nope... but what invitation are you talking about?
merci madame or monsieur
playwrights
The French word for "invitation" is (drum roll, please): "invitation."
Une invitation d'anniversaire (literally "an invitation of birthday").
It seems like there was a typographical error: perhaps you meant to say "declined." To decline typically means to refuse or reject something, such as an offer or invitation.
I ruefully had to refuse the invitation as I had a prior appointment