The coronavirus pandemic has "exposed every fracture" in U.S. workplace safety requirements as essential workers are infected and die of Covid-19, several of the country's largest unions and a former worker safety official under President Barack Obama said Tuesday.

Even as most states have rolled out social distancing restrictions to curb the spread of Covid-19, the country's essential workers, from health-care providers and grocery workers to meatpackers and steelworkers, have continued to punch into work. Now some of the country's largest unions are calling for emergency regulation to ensure worker safety.

"You would not think that our professionals would be the ones who are screaming from the rafters about the failure of OSHA to do its job," Randi Weingarten, president of the American Federation of Teachers, said of the Occupational Safety and Health Administration. The union also represents health workers. "But I am mad."

Weingarten and other union leaders joined together to call for OSHA, an agency that polices workplace safety within the Department of Labor, to implement enforceable emergency coronavirus workplace regulations. The union representatives spoke on a conference call with members of the press to commemorate Workers' Memorial Day.

"Under this administration, OSHA's response for America's workplace safety has left workers to fend for themselves during the biggest health crisis in recent history," United Steelworkers Secretary-Treasurer John Shinn said. "Instead of inspecting and fining employers, the agency is merely asking employers to investigate complaints against themselves and take corrective action."

All of the union officials on the call, who collectively represent more than 6 million American workers, criticized OSHA for not acting more quickly to investigate workplace complaints related to Covid-19. The Washington Post reported earlier this month that workers have filed more than 3,000 such complaints.

The agency announced earlier this month that it's unlikely to investigate employers except for high-risk workplaces such as hospitals. Rather than overseeing its own investigations, the agency is encouraging employers to respond to worker complaints on their own, said David Michaels, who led the agency during the Obama administration.

Representatives of OSHA did not respond to CNBC's request for comment.

"Even an enthusiastic OSHA would be fighting with one arm tied behind its back," Michaels said. "The agency is under-resourced, and the standard-setting process is lengthy and Byzantine, so many hazards are unregulated. OSHA's weaknesses have been magnified under President [Donald] Trump."

OSHA has gone without a nominee for assistant secretary for more than three years, Michaels said, adding that half of the agency's leadership positions are empty.

Rep. Rosa DeLauro, D-Conn., former assistant secretary of Labor for OSHA, introduced legislation last week that would compel OSHA to issue temporary emergency standards to protect employees against exposure to Covid-19.

"The failure, quite honestly, of OSHA to protect workers didn't start with this pandemic," said DeLauro, who serves as chair of the Labor, Health and Human Services appropriations subcommittee. "But I believe it can be forcefully argued that it is just failing to adequately address this particular crisis."