The animal rights org fired off a handful of letters over the past few days -- all obtained by TMZ -- and they're aimed at the director and his big-ticket cast ... Pedro Pascal, Denzel Washington, Paul Mescal and others.

In the correspondence to Ridley, PETA says it's received whistleblower complaints alleging he's using both horses and macaque monkeys on set while shooting in Malta ... including a claim at least one of the horses recently collapsed. PETA is presuming the alleged collapse is due to extreme temperatures on the Mediterranean island.

It says, "Scorching summer heat and oppressive costumes are a dangerous mix for horses, who are naturally skittish animals, prone to flight and injury, and vulnerable to the stresses of a film set. The film and TV industries have a past riddled with on-set horse injuries and even deaths. We sincerely hope Gladiator 2 avoids adding another death to that list."

PETA also lists the dangers of working with live macaques, saying they're unpredictable and can hurt humans. They also say these monkeys are often ripped from their mothers at a young age for these types of film settings ... calling their alleged use unethical.

Despite the SAG-AFTRA strike, PETA says it's heard rumors "Gladiator 2" is continuing production this week, and asks Ridley to leave live animals out of it completely, suggesting he use CGI animals instead.

We've reached out to Ridley, Paramount, and the production company behind 'G2' ... so far, no word back.

BTW, we're told a similar letter was fired off to all the actors attached to 'Gladiator 2.'