Thank you very much indeed.
それは誠に残念なことです。
That is truly regrettable.
誠に申し訳ありません。
I am sincerely sorry.
I am truly sorry.
We regret to inform you that you were not selected this time.
真に is a modern formal/literary word meaning 'truly', whereas 定 (さだ) carries the same sense but is confined to archaic or classical usage.
誠に is a very formal, polite adverb often used in apologies and greetings (誠に申し訳ございません), while 真に focuses on genuine, essential truth rather than politeness.
Rarely used kanji form.