Cousins' collision with Posey in a May 25 game resulted in leg and ankle ligament injuries to the Giants' receiver that will keep him out for the rest of the year.
A backlash against Cousins intensified this week when Giants General Manager Brian Sabean said on a local radio show, "If I never hear from Cousins again, or he doesn't play another day in the big leagues, I think we'll all be happy."
Cousins has said he has received death threats in the wake of the incident.
Posey reiterated in a statement Saturday he doesn't blame Cousins and wishes everyone would "move on."
"I appreciate the continued support of Giants fans and others as I begin the process of working my way back. But in no way do I condone threats of any kind against Scott Cousins or his family," Posey said.
The catcher said he hadn't talked to Cousins but was aware "he made the effort to reach out to me on the night of the play."
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend