To view the video, click here
The fight takes place in their home country, the Dominican Republic, where cockfighting is legal and popular. It is banned throughout the United States.
Martinez told the Mets the cockfight occurred at least two years ago.
In the wake of Michael Vick's recent dogfighting case, Martinez and Marichal are the latest sports stars to draw criticism for animal fighting.
People for the Ethical Treatment of Animals sent letters to both pitchers Thursday, calling on them to publicly apologize. The Humane Society of the United States said "Major League Baseball should join us in condemning Martinez and Marichal for their shameful example."
"I understand that people are upset, but this is part of our Dominican culture and is legal in the Dominican Republic," Martinez said in a statement issued by the Mets. "I was invited by my idol, Juan Marichal, to attend the event as a spectator, not as a participant."
In the video, which was posted Tuesday, the animal released by Martinez appears to be killed. The fight takes place in the Coliseo Gallistico de Santo Domingo (Santo Domingo Cockfighting Coliseum) in Santo Domingo, the Dominican Republic's biggest cockfighting venue.
By early Thursday, the video was removed "due to terms of use violation."
PETA also sent a letter to baseball commissioner Bud Selig urging all major league players and staff to take its animal sensitivity training course - the same one Vick attended after pleading guilty to federal dogfighting charges in August.
The Atlanta Falcons quarterback received a 23-month jail sentence. The NFL suspended him indefinitely without pay.
In his letter to Selig, PETA assistant director Dan Shannon mentioned the Vick case and wrote, "it seems that education on the importance of treating animals humanely is in order for Major League Baseball."
Baseball spokesman Rich Levin said Selig had not yet seen the letter.
"We don't condone any kind of animal cruelty, but we're not going to comment on any individuals at this time," Levin said.
Wayne Pacelle, president and CEO of The Humane Society, released a statement admonishing Martinez and Marichal.
"Animal fighting has no place whatsoever among those who presume to be role models for youngsters, not in this country and not elsewhere," he said. "Pedro Martinez and Juan Marichal exhibited appallingly bad judgment in participating in a staged animal fight. It doesn't excuse the behavior to find a legal haven for this reprehensible and inhumane conduct. It's animal cruelty, no matter where it occurs."
Pacelle also referred to Vick's case.
"Michael Vick brought home the lesson when his career was ruined by disclosures of his involvement in a dogfighting ring. Cockfighting is a similarly barbaric activity that forces two animals to mutilate and kill each other with sharp weapons strapped to their legs," he said. "There is no moral distinction between dogfighting and cockfighting - both involve the torture of animals for the titillation of spectators who enjoy the violence and bloodletting."
Pacelle called on the Mets "to take appropriate action to distance themselves from Martinez's behavior."
"We do not condone any behavior that involves cruelty to animals," the Mets said in a statement. "We understand, however, that in many other countries activities such as bullfighting and cockfighting are both legal and part of the culture."
Except for baseball, cockfighting is widely considered the Dominican Republic's most popular sport. Almost every small town along the Caribbean nation's highways boasts a covered fighting ring where trainers come to test their best roosters and rich and poor alike fill the wooden stands to drink, wager and watch the bloody spectacle.
One of the best-known fighting rings is in Martinez's hometown of Manoguayabo, made famous in 1991 as the opening setting for Michelle Wucker's noted history of the Dominican Republic and Haiti, "Why the Cocks Fight."
The island's fighting Mecca is the Coliseo Gallistico de Santo Domingo, a sparkling indoor arena on the outskirts of the Dominican capital where fights are tracked on an electronic scoreboard and waitresses walk the aisles with trays of beer and empanadas. Generals, politicians and cockfighting celebrities have their names painted onto assigned parking spaces outside.
On fight days, well-heeled Dominicans and curious foreigners - almost all of them men - put on their best suits, polo shirts and chacabanas for a card with as many as 30 fights. Between bouts, bettors tour the fiberglass cages where prime roosters are examined with the same keenness of eye as a regular in the paddock at Churchill Downs.
The fight begins when two roosters are lowered into the arena. Men in blue or white coats more at home in a laboratory or butcher shop prep the fighters, taunting them into a frenzy with a third rooster. As the timed fight begins, the crowd erupts in a flurry of one-on-one betting, flashing hand signals across the room to signal fast-changing odds with the ironclad frenzy of a New York trade floor.
Roosters are generally armed with a small bone or resin spur meant to inflict maximum damage on their opponents, and the blood, feathers and poultry stench that linger afterward are a testament to their potency.
But the roosters do not always die. Matches are timed, 10-15 minutes in length, and many end in a draw with both chickens bloodied and exhausted, but alive to fight another day.