"Immediate apology" refers to saying sorry without delay, right after realizing a mistake or after someone points it out. It means expressing regret or admitting fault immediately, without any hesitation. Full definition
POLITICO New York also reported that Officer James Frascatore earned nearly $ 10,700 in overtime pay in the last fiscal year, even though he was placed on modified duty for tackling retired tennis star James Blake on September 9, 2015, in a case of mistaken identity — an incident that prompted de Blasio and Bratton to issue immediate apologies. (politico.com)
When it's obvious you've made a bad impression, often the best course of action is to issue an immediate apology. (entrepreneur.com)
The pre-match preparations were marred by an incident in which City's bus was damaged by projectiles thrown from the raucous Liverpool crowd gathered outside the stadium, with the club issuing a full and immediate apology to (liverpooloffside.sbnation.com)