One of the victims was 40-year-old Amy Martich of west suburban Elmhurst.
The race director says she is believed to have gone into cardiac arrest twice after Sunday's swim
People hoping to take part may have to give more documentation on their training and experience in the future. The race includes a mile swim, 25-mile bike ride and six-mile run.
Michael Kudryk, 64, of Freehold, N.J., also died Sunday after he was pulled out of the Hudson River unconscious. Police say he was believed to have suffered a heart attack.
The deaths were the second and third ones at the popular triathlon in the last three years. On Monday, a New York City lawmaker called for a top-to-bottom review, questioning whether rain the night before -- which could have led to choppy water and strong currents -- or 90-degree temperatures were factors.
Race director Bill Burke called the deaths "a very, very sad occurrence and tragedy," but characterized the weather conditions during Sunday's race as optimal, with relatively mild temperatures and good cloud cover for much of the day. The temperature reached 89 degrees in Central Park on Sunday with high levels of humidity, according to the National Weather Service.
Burke said participants were not required to provide a health certificate or proof that they have participated in another triathlon -- things he would like to see enacted in the future.
"It's something we're going to look at and try to put possible identifiers in place that can hopefully give us some indication and let the athletes know what they need to be careful about," he said. "Have you done an open-water swim? Have you participated in another triathlon? How much training have you put into this?"
Burke said it was not uncommon for some people to struggle with over-exertion. He said he most commonly sees heat-related problems like fatigue and dehydration.
"What we try to do at all of our events it to give the athletes as much knowledge as possible," he said. That includes posting information on the event website and emailing potential competitors about different training programs taking place in their communities that might better prepare them for the event.
"I already talked to the USA Triathlon this morning," Burke said. "We're certainly going to take a very hard look at everything, at how people prepare for this."
Three years ago, a 32-year-old competitor from Argentina was pulled from the water unconscious and later died. The medical examiner ruled that he died from hypertensive cardiovascular disease, a condition linked to high blood pressure. Race organizers said he apparently was unaware of his condition.
Manhattan Borough President Scott Stringer asked triathlon organizers to conduct a full review.
He cited a 2009 study by the Minneapolis Heart Institute that found athletes participating in triathlons have twice the risk of sudden death as those running in marathons. He also pointed out a recent study published in The Journal of the American Medical Association that found 14 people died while participating in triathlons, 13 of them while swimming, from 2006 to 2008.
"New Yorkers signed up for a triathlon -- not a game of Russian Roulette," Stringer said. "Choosing to compete is a decision every athlete has to make for themselves, but it is the obligation of the city to make sure all potential risks are accounted for to the extent possible."
Dr. Kevin Harris, a cardiologist at the Minneapolis Heart Institute and lead author of the 2009 study, said anyone with risk factors for heart disease should get checked out before competing in a triathlon. Training is also crucial, particularly because it's difficult for participants to rest in the water if they start to tire, he said.
While it's difficult to replicate the conditions of a group swim, training in a larger body of water like a lake instead of a pool can help.
The triathlon has grown in popularity. Burke said more than 3,000 people participated in Sunday's race, the 11th one held, compared with 683 the first year. Athletes are selected via a lottery system, similar to major marathons.
Burke said safety was always the triathlon's No. 1 concern. For example, he said, in 2003, the swim portion was canceled due to high bacteria levels in the water.
In Central Park on Monday, several athletes said the news was unsettling but would not deter them from participating.
Annette Kiider, a 36-year-old personal trainer, said she entered the lottery for this year's New York City Triathlon but didn't get a spot.
"I still want to do it," she said. "I feel like the New York triathlon would be different and exciting. I know with the New York marathon, there's just so much energy."
John Egan, 33, said he had participated in triathlons and open-water swims. He said the "bunch start" where swimmers all dive into the water at once can be scary and disorienting. But the New York City triathlon already uses a more orderly system where 20 swimmers jump in at once.
Egan said he didn't think race organizers should be tasked with screening participants.
"If you choose to do it you should know your limits," he said. "I don't feel like it's the race organizers' responsibility. I feel like that's untenable."
The Associated Press contributed to this report.