I'm afraid Mr. Perkins is ____________ at the moment; he seems to be in a meeting.

The most suitable choice for the sentence is "Unavailable." Using this word effectively communicates that Mr. Perkins cannot be reached or is not able to attend to others due to his current engagement in a meeting. It implies that he is not in a position to interact, which aligns perfectly with the context provided in the sentence.

The other words, while related to being occupied or engaged, do not fully capture the notion of not being reachable in the same way "unavailable" does. For instance, "present" suggests that he is physically there but does not imply he can be contacted, while "busy" and "occupied" convey that he is involved in something, yet they do not carry the same connotation of being inaccessible. Hence, "unavailable" is the most precise term for this scenario.