LONG ISLAND, New York (CNN) -- The death of a temporary Wal-Mart worker trampled by customers amid frantic Black Friday shopping could have been avoided, the union that represents retail workers said Saturday.

Jdimytai Damour, 34, was crushed as he and other employees attempted to unlock the doors of a Long Island, New York, store at 5 a.m. Friday, police said.

"This incident was avoidable," said Bruce Both, president of the United Food and Commercial Workers Union Local 1500, the state of New York's largest grocery worker's union.

"Where were the safety barriers? Where was security? How did store management not see dangerous numbers of customers barreling down on the store in such an unsafe manner?

"This is not just tragic; it rises to a level of blatant irresponsibility by Wal-Mart," he said. Watch father of trampled worker react »

Wal-Mart spokesman Dave Tovar said Saturday that the company had no response to the union's comments, referring CNN to a written statement the retailer released Friday.

The statement said the store added internal security, brought in outside security, erected barricades and worked with Nassau County police in anticipation of heavy crowds.

"Our thoughts and prayers go out to the family of the deceased," Wal-Mart Senior Vice President Hank Mullany said in the statement. "We are continuing to work closely with local law enforcement, and we are reaching out to those involved."

Damour's death was one of two high-profile violent incidents on Black Friday, the day after Thanksgiving and traditionally one of the year's busiest shopping days.

Police say two men shot each other dead in a Toys "R" Us in Palm Desert, California, after they argued in the store. The fight did not appear to be related to shopping, according to authorities.

At the Wal-Mart, police say that a line began forming at 9 p.m. Thursday and that, by 5 a.m. Friday, there were as many as 2,000 customers outside. A video showed about a dozen people knocked to the ground as the doors were opened and the crowd surged, breaking the doors.

Minutes later, police trying to give Damour first aid were jostled by customers still running into the store, authorities said.

The union is calling for an investigation "by all levels of government" to ensure justice for Damour's family and make sure that such an incident never happens at Wal-Mart again. Watch reaction to the incident »

"If the safety of their customers and workers was a top priority, then this never would have happened," said Patrick Purcell, a projects director for the local UFCW. "Wal-Mart must step up to the plate and ensure that all those injured, as well as the family of the deceased, be financially compensated for their injuries and their losses. Their words are weak."

The UFCW has long been a harsh critic of Wal-Mart's, arguing that the world's largest retailer offers low wages and poor health care for its workers and pushes competitors and suppliers to do the same or go out of business.

The group has had only marginal success in organizing Wal-Mart workers in the United States and Canada, citing aggressive anti-union efforts by Wal-Mart.

The UFCW has 1.3 million members working largely in the retail, food and food-processing industries.

CNN's Leslie Tripp contributed to this report.

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