MT_Head's answer is spot on — saying "I'm full" isn't rude.
I don't think there is another single word that is similarly polite and well-understood.
If you want to avoid saying "I'm full", you could say things like, "I've had plenty," or "I've had too much already."
Host: "Would you like any more?"
Guest: "Oh, no thank you, I've had
plenty. This was all wonderful, thank
you."
Or...
Host: "Do you care for seconds?"
Guest: (leaning back) "Oh, no I can't,
I've had too much already. Thank you,
it was delicious!"
Or...
Host: "Please help yourself, there's
plenty more."
Guest: "Oh, no, don't tempt me!"
( in a joking / laughing manner )
"No, I better not, thank you. This was all fantastic!"
All of these are ways to avoid saying "I'm full" which would sound natural. However, be prepared that "I'm full" is probably the keyword your host is looking for, so if they insist...
Host: "Are you sure? There's more dessert!"
Guest: "No, no I really can't. I'm perfectly satisfied right now, if I ate any more it would be too much."
In this way you can imply to your American host that you are not turning down the food because it isn't good, but because you really have eaten all you would like to eat — or even a few bites too much.
Really I think what this (sadly) reflects is that we Americans are prone to eating too much food when we really like it, so if you don't seem to have eaten "a little too much" your host may wonder if the meal wasn't to your liking.
So, while you don't have to say it yourself, it's probably best to understand that this is reason people in America say "I'm full." You're indicating to the host that the food was so irresistible you already had a little bit too much, and now you really must decline (or risk being sick!).
As an American this isn't part of my culture that I'm especially proud of, but it is what it is, and it's better to understand than to remain uncomfortable with it.
I hope this helps! Good question, by the way :)
Irrespective of whether most people in a certain region find it polite or not, if you are dealing with a customer and one you've probably not interacted with before, your best bet - more so from a business perspective, is to use safer alternatives, such as beg your pardon?.
Some might say I'm not answering the question and going tangential, but I think perception of rudeness can be subjective and therefore not just within in the realm of grammatical correctness.
Best Answer
You should say that the requirements are mutually exclusive. Here are a couple examples:
(From MWLD)
(From Forbes)