Rep. Jerrold Nadler said he was going to register. Assemb. Michael DenDekker said he already had.

The Manhattan and Jackson Heights Democrats endured sweltering heat Friday along with advocates and union members gathered on the steps of City Hall to urge anyone who helped in the rescue, recovery and cleanup of the World Trade Center to register by Sept. 11 -- Thursday -- with the New York State Workers' Compensation Board to preserve their ability to file a claim.

Workers can file a WTC-12 form whether they were employed or volunteered and regardless of whether they are healthy or sick. This includes those who worked at Ground Zero, Fresh Kills Landfill, the barges, the piers and the morgues. The form must be notarized.

"Whether you volunteered or worked for a union, you can register," Nadler said. "It does not mean you have to be ill."

Rachel McEneny, a spokeswoman for the workers' comp board, said 41,000 workers or volunteers had registered so far but no one knew how many more were eligible.

That's in part because many workers were subcontracted by other employers and volunteers just showed up, said Kandace Vallejo, World Trade Center outreach coordinator for the New York Committee for Occupational Safety and Health, the workers' advocacy group that sponsored the event. And many -- especially those involved in cleanup -- were undocumented. Immigration status does not affect a person's ability to register, she said.

Some World Trade Center workers also are facing another deadline: Anyone diagnosed with a 9/11-related cancer other than prostate cancer on or before Oct. 12, 2012, must register with the federal Victim Compensation Fund by Oct. 12. [Those diagnosed with prostate cancer on or before Oct. 21, 2013, have until Oct. 21, 2015 to register.]DenDekker, a city Department of Sanitation employee on Sept. 11, 2001 who worked eight months on the pile, said he registered with the workers' comp board right away. Although he remains healthy, he said he had many 9/11 colleagues who had succumbed to illness.

"Every year we gather at the 9/11 site," he said. "Every year I notice there's one less person."

Nadler apparently hadn't thought of himself as someone who could register with the workers' comp board until he asked about it. As a congressman, he said he had been on the World Trade Center site many times in the days following the attacks.

"I'll do it online," he said.

For a copy of the form, go to www.wcb.ny.gov. People can also go to their local workers' comp board.

On Sept. 10 the charity Voices of September 11th is hosting an all-day information forum at the Marriott on 85 West St. in Manhattan, where people can get help registering. Notaries will be on hand.