That is not the word "whisper". I find that writing "He said softly" fits the best, but it has an adverb.
What's the context? Maybe it's better to come in before the speech - His order was barely audible. "Don't you move a muscle." - example.
The character is angry, but another character says something concerning. He's trying to calm her and it should show the reader he's no longer angry and concerned about what she said. More specifically, character just broke up with his girlfriend. His young daughter saw them arguing and later asked if girlfriend hated her. He reassures her that girlfriend does not hate her. (It's actually more complicated than that.)
"softly" or "gently" is one of those adverbs I would personally use. There's something very sweet about it that a stronger verb just doesn't deliver - perhaps because the idea of being "soft" goes well with the "weaker" impact of an adverb, I'm not sure. Only you know the context of your passage - read through it and if "softly" fits, then go with it. Adverbs are good when used appropriately, and forget about those who claim you should "never" use adverbs. There's never any "never"s in writing But if you really want, here are some useful verbs: - He breathed - He murmured - He muttered - use a phrase such as Peach suggested above, or something like "His voice was soft/quiet/a whisper" etc - He said (being neutral is fine - the dialogue itself should convey enough) - No tag at all (let the dialogue do the job and forget about adding any kind of detail - the atmosphere and context of your piece, if the writing is strong enough, should allow for this to be just as effective, depending on what else has gone on before)
Adverbs aren't bad in their proper place, and that one is where it needs to be. Where they cause problems is where the meaning is the same with or without them, or where, in speech, they would be demonstration words. There's no difference between silence and absolute silence. But in speech we use it to add emphasis, as in, The room was ab-so-lutely silent. But would you rewrite the line, "Killing me softly with his song," because it contains an adverb? I sure wouldn't.
It's when we say something like, "He turned, sloooooly," to illustrate the mood we want the word to set. But in print, in most cases, "he turned" is more than enough because the reader can't see it happening, and including mention makes it seem contrived. Only if it's done deliberately or the speed matters should the word be included in the printed version.
Adverbs are not inherently bad. They have a place and a time, as does everything. Out of preference I would probably avoid "... he breathed." It just sounds corny to me. "Mumbled" and "muttered" should also be reserved for when something is specifically being mumbled or muttered. I think the tone of the scene should help establish the volume of the conversation. Also, as @peachalulu suggested, giving a cue before the line is another possibility. Just avoid cluttered dialogue tags.
I'm right now having fun visualising all the ridiculous ways I could "unpack" the adverb Can you imagine!?
