Vehemently means with very strong and forceful feeling. Said hard, and meant harder.
It attaches almost entirely to denial and opposition, so vehemently denied and vehemently opposed account for most uses of the word, and both belong to reporting. The strength is in the delivery rather than the argument, which is worth noticing, since a vehement denial proves nothing except that somebody minded. The adjective vehement and the noun vehemence follow the same pattern.
1adverbvehementlyWith intense and forceful feeling.
“He vehemently denied ever having seen the letter.”
From vehement + -ly.
Etymology from Wiktionary, CC BY-SA