Disculpas (in English, ‘apologies’ or ‘excuses’) is defined as the reason that is given or the cause that is alleged to excuse or to purge a fault.  So, with said meaning in mind, it is logical that the actions of giving, offering, asking, begging, pleading, etc. for such apologies are viable and admissible scenarios. So, since pedir disculpas would be equivalent to ‘asking for forgiveness’ and ofrecer disculpas would translate to ‘offer apologies’, then both would be grammatically correct phrases in the context of expressing one’s apologies in Spanish. Note how in the example, pedir disculpas and ofrecer disculpas are practically interchangeable: Pido disculpas por mi comportamiento. (literally, I ask for your forgiveness for my behavior and more aptly translated to ‘I apologize for my behavior.’) Ofrezco disculpas por mi comportamiento. (literally, I offer you my apologies for my behavior and more aptly translated to ‘I apologize for my behavior.’)