A formal expression used in official statements, diplomatic language, or polite apologies to convey regret or disappointment. Often appears as 遺憾の意を表する (to express regret).
The government expressed regret over this decision.
彼の辞任は遺憾の意をもって受け入れられた。
His resignation was accepted with regret.
A Sino-Japanese compound: 遺憾 (regrettable) + の (possessive particle) + 意 (intention, feeling). The phrase is a fixed formal expression.