I haven't been able to find a satisfying answer explaining Etzali's and Misaka's reactions yet, so...
Whatever he said, it obviously confirmed the promise Etzali asked for, but it wasn't what he had wanted to hear.
Combined with Misaka's reaction, I have two theories. I'll start with the one that's less likely:
In A Certain Magical Index II episode 23, Kamijo says to Kazakiri that he'd rather chop his hand off than lose one of his friends. I am mentioning this because it shows that he would make a statement essentially comparing the value of body parts and people, even though it specifically makes sense in that context because his right hand can literally kill Kazikiri.
The idea is that maybe he said something along the lines of "I'll protect her like my right hand" or "I'd chop off my right hand for her".
The reactions would then basically be a masturbation joke. I honestly don't find this theory very satisfying.
Luckily, there is evidence to contradict it. Here is the excerpt from the light novel, copied from Reddit:
Mikoto and the boy were the only ones in the alley.
The words that had come out of his mouth shook her more than she let on. But what rocked her very core—that she did not realize. Nevertheless, she unconsciously understood that she’d be better off not letting it show. Or rather, she possessed a compelling force telling her that she mustn’t do so.
However, without care, it would erupt within her. She was desperately holding it back, like a raging vortex of steam trying to escape her body.
It was strange.
She didn’t want to let it show on the surface, but she felt pained trying to hold it back.
Would that not mean that deep down she wanted to let it show? But that wasn’t the case.
Just thinking about letting it show nearly made her red in the face.
And she didn’t even know what the essential thing was.
She held everything in her throat, not understanding why.
One way or another, she’d realized it.
Mikoto had always kind of thought she was a unique existence. She had thought that even her distance to this boy had shrunken just a little bit compared to everyone else. Like if he was browsing a list of a thousand names and saw the name Misaka, he’d at least stop for a moment.
But no—she’d been wrong.
And that fact by itself had a big effect on her. She didn’t even understand why something as insignificant as this had caused her so much damage, so she of course couldn’t think of a way to deal with it. She wanted to run away right now if she could—from this unidentified pain.
But she couldn’t.
She didn’t want to turn tail and run away from him.
It would hurt him.
The pain would be much more than what she was feeling now.
(…Man, I really am an idiot, if I do say so myself.)
In my opinion, the marked part sums up the meaning behind her reaction. She realizes that to him, she's more or less just another person.
This makes me think that he said something along the lines of "I'll protect her like everyone else" or "I will protect everybody I can".
The idea is that this would be the worst possible answer because Etzali wanted him to commit specifically to protecting Misaka, but it still gives the promise because it includes him protecting her.
Now, in the anime, Misaka also says that she is taking what he said the wrong way and that he made it very misleading. The idea with that is that Kamijo is the kind of guy who protects people wherever he can, but this doesn't actually mean he cares about everyone equally. He still likes some people more than others, but he protects everyone.
It should also be noted that, in the light novel, he actually realized Misaka was close because he is so unlucky that he wouldn't have survived otherwise:
A steel girder had fallen into the ground right between his legs as he sat on his butt. That wasn’t all. All around him, more of them were sticking out of the ground, covering them up, like a badly made hut with tons of holes in the roof. There was a precarious balance here that seemed so weak a breeze would cause the whole thing to come crashing down, but for now, at least, Kamijou hadn’t been buried alive.
(That was lucky…wait, that’s impossible. I’m unlucky, after all. Which means…oh, I see. That Level 5 can use the power of electricity to manipulate magnetism, too, can’t she?)
However, this doesn't seem to affect what he says to Etzali at all, he either didn't think about it much or simply didn't care if Misaka heard his answer in the way he gave it. I do feel like this is in line with his character.