apologise unreservedly

Translations
безоговорочно извиняться
They apologised unreservedly for the inconvenience caused.
Они безоговорочно извинились за причинённые неудобства.
Definitions
To express regret or remorse without any conditions or reservations, fully acknowledging one's wrongdoing and taking complete responsibility for it.
Words
apologise

verb
извиняться
unreservedly

adverb
безоговорочно