The rock band's longtime drummer issued a statement Sunday, which has some encouraging updates on his condition. He says, "Thank you everyone for your overwhelming support. Your love and prayers are truly helping. My wife Lauren [Monroe] was thankfully not with me at the time of the incident. We are together now, and working on recovering in a safe space."

According to ABC News, which obtained his remarks, Allen and his family are now shifting their attention toward "healing for everyone involved" ... although he doesn't really elaborate.

There's more ... RA goes on to say, "We ask you to join us in our effort to move from confusion and shock to compassion and empathy. We understand this act of violence can be triggering for so many people."

He finishes with ... "To all of the fans, veterans and first responders in our global community, we are thinking of you all. Together with love, we can all get through these difficult times."

Allen never mentions his alleged attacker by name -- 19-year-old Max Hartley, whom police claim was the one who beat Rick down -- but it does seem he's alluding to him ... and, perhaps, there's more to the story.

In any case, it's great to hear he's doing okay. You'll recall ... the incident was described to cops as brutal. Hartley is accused of bum-rushing Rick at a hotel in Ft. Lauderdale, allegedly knocking him to the ground and going on to attack a woman who was nearby too ... according to the arrest report. The dude was booked for battery, among other charges.