did not accept, did not agree to
彼は彼らの招待に応じなかった。
He didn't accept their invitation.
何もかも買収しようとして応じなかったのは殺された
Those who refused to go along with the attempt to buy everything off were killed.
— ロシアン・ブラザー (1997)
彼から招待状をもらったがそれに応じなかった。
I received an invitation from him, but I declined it.
竹内だけは招待に応じなかった。
Takeuchi was the only one who didn’t accept the invitation.