I'm not sure you can say someone offers a promise in English. It's understandable but the common phrase is to make a promise, which I think should be accepted.
It seems to be not too common, but possible, after a short search. In fact I can see some difference in the semantics, at least in Czech.
What would the difference in Czech? In English I can imagine someone saying that only in special circumstances as a rhetorical device. For example: We asked him for help but he offered a lot of promises instead. The verb offer is contrasted with the help that is not being offered. However, if you just want to talk about someone making a promise you wouldn't use offer.
'Offered' seems to me to mean that the receiver of the promise distrusts the promise, while 'made' seems neutral or trusting of the promise
DL seems to ignore paragraph marks for some reason. Sorry for the ugly lump of text.