My sincerest apologies for the error.

Meaning

A formal and sincere apology for a mistake.

Examples

• John: 'There was a mistake in the report, Alice.'
• Alice: '<b>My sincerest apologies for the error</b>; we'll correct it immediately.'
• John: '<b>My sincerest apologies for the error</b>; we'll issue a corrected version.'
• Alice: 'The figures were incorrect, John.'