-he did say that. -he said that. The difference is that 'did say' adds emphasis or confirmation, for example if the 'guys' had expressed doubt or surprise that you said that, or you had not been sure whether you had said it. Further emphasis could be provided by preceding 'did' with an adverb such as really, actually or definitely.

Hello there, I totally agree with Katya's explanations and examples. Both sentences are correct, the second choice is used in the case of emphasis. More examples: Are you sure about seeing your teacher ? YES! I DID see him in the bus. *** Are you kidding me? NO, I swear, I DID break up with her! *** Did you close the window? Are you sure? YES, I DID close it.

You usually use an auxiliary verb like "did" for emphasis.