There were heated exchanges after Spanish fighter Martinez said he has come to Belfast to shut Frampton's mouth.
"We'll see how strong you are when I'm hitting you on the chin," the local man responded.
Martinez has pulled out of the European Super Bantamweight contest twice in the last 18 months but blames internal issues in his camp for that.
"I'm here," he told Frampton at the press conference on Thursday.
"It wasn't my fault I wasn't here the last time but I'm here now. I've come here to shut Frampton's mouth once and for all.
"He's talked too much and on Saturday I hope he comes to box and not to run."
Tiger's Bay brawler Frampton, who's managed by former world champion Barry McGuigan, said he isn't running anywhere.
"We'll see how strong you are when you get hit with the hardest punches you've been hit with in your life," he replied.
"We'll see if you want to run. I'll stand in front of you and I'll outbox you, outpunch you - do whatever you want."
The pair are set to go head to head at the Odyssey Arena this weekend.