expression, noun
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).
政府は今回の決定について遺憾の意を表した。
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.
残念 is a common, everyday word for 'regrettable' or 'too bad'. 遺憾の意 is much more formal and used in official contexts.
A Sino-Japanese compound: 遺憾 (regrettable) + の (possessive particle) + 意 (intention, feeling). The phrase is a fixed formal expression.