Incognito is accused of being the ring-leader in a situation that forced Martin to leave the team due to persistent harassment, and the 30-year-old is currently under investigation by the NFL over the incident.
However, in his first in-depth interview since being suspended by coach Joe Philbin, Incognito claimed that his treatment of Martin was merely the nature of their relationship.
"When words are put in a context, I understand why a lot of eyebrows get raised. But people don't know how Jon and I communicate to one another," Incognito told Fox Sports.
"For instance, a week before this went down, Jonathan Martin texted me on my phone, 'I will murder your whole fucking family.' Now, do I think Jonathan Martin was going to murder my family? Not one bit.
"He texted me that. I didn't think he was going to kill my family. I knew that was coming from a brother. I knew it was coming from a friend. I knew it was coming from a teammate."
In the interview, Incognito also admitted that he regrets using racial slurs towards Martin, but claims that such language is created by the locker room environment.