The death toll among those sickened by the toxic dust and ash of Ground Zero will within as little as five years exceed the number of people killed on the day of the 9/11 attacks, experts say.

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As those who lost loved ones at the World Trade Center, at the Pentagon and on Flight 93 gather for Sunday’s 15th anniversary of the terror attacks that killed almost 3,000 people, a post-9/11 health crisis is growing.

At least 1,000 people – and probably many more – have died often lingering, painful deaths resulting from illnesses related to their exposure to debris that spread from the wreckage of the World Trade Center towers in downtown Manhattan. More than 37,000 are officially recognised as sick.

Calls are growing for a new monument to be added to the World Trade Center site, to pay tribute to those who have died or become sick since 9/11 because of toxic exposure.

“Within the next five years we will be at the point where more people have died from World Trade Center-related illnesses than died from the immediate impact of the attacks,” said Dr Jim Melius, a doctor at the New York State Laborers Union who also advises the White House on worker health, chairs the steering committee overseeing the government health program for 9/11 responders, and is a member of the advocacy group 9/11 Health Watch.

“There are a lot of people who are very, very ill with lung disease who will see at least 10 years taken from their normal life span,” he said, “and we are already seeing many more premature deaths occurring, and among younger people, from the cancers. There is going to be a new generation of widows and widowers.”

In 2001, government officials, most prominently the then head of the Environmental Protection Agency (EPA), Christine Todd Whitman, assured those in lower Manhattan in the days after the attacks that the air was safe.

In an interview with the Guardian this weekend, Whitman said for the first time that in hindsight she had been mistaken. She apologised to those affected by the toxic debris.

After al-Qaida terrorists flew hijacked passenger jets into the north and south towers of the World Trade Center, the towers collapsed. Clouds of fumes and debris billowed out over New York City. Of 2,977 people killed in the attacks, 2,753 died at the World Trade Center.

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The debris left by the twin towers, the main concentration of which became known as “the pile”, contained asbestos, lead, glass, heavy metals, concrete, poisonous gases, oil and other dangerous substances that mixed with exploding jet fuel, the contents of hundreds of offices and dead bodies to fill the air and cover the area around the site.

“It was disgusting,” said Merita Zejnuni, 52, a cleaner who was working a few blocks from Ground Zero in the offices of banking giant Goldman Sachs on the morning of 9/11. “It coated your mouth and your throat. I was covered in it – I looked like a ghost.”

Zejnuni developed a violent, chronic cough and was recently found to have breast cancer. This weekend, speaking to the Guardian, she gave her first interview. Her lawyer, Troy Rosasco, said Zejnuni only found out last month she could apply for compensation. Rosasco believes thousands of other people are sick or dying as a result of exposure around Ground Zero, away from the public eye.

“There is a general consensus that people down there got huge exposure,” he said, “but many don’t even know why they are sick.”

Last month, researchers at Stony Brook University announced that cognitive impairment, a leading risk factor for Alzheimer’s disease, was being detected among first responders who went to Ground Zero on and around 9/11.

“That’s scary news,” said Rosasco. “I have probably gotten 50 calls in the last two days from people who are really frightened about that.”

In 2010, after years of political battle, Congress passed the $4bn Zadroga Act – named for a police captain who worked on rescue efforts at Ground Zero and died in 2006 after developing breathing problems – to cover the health costs of those poisoned by the debris and fumes of 9/11. Late last year, it agreed to extend the act’s provisions for 75 years. There is a separate, official Victim Compensation Fund.

In 2011, the federal World Trade Center Health Program (WTCHP) was established. It has 75,000 registered members, 87% of whom worked on rescue, recovery and clean-up. The rest are New York residents or workers. A total of 1,140 registered members have died since the program was created in 2011, WTCHP spokeswoman Christy Spring said.

“Because of the way the legislation was written,” she said, “there is an understanding that there is a link between the exposure and the illnesses people are suffering from.”

Causes of death are not recorded by the WTCHP. There is no central record for how many people died between 2001 and 2011 from illnesses linked to 9/11 fumes and debris, Spring said, nor any way of knowing exactly how many other people have died without any record of their illnesses having been caused by exposure near Ground Zero.

Melius said: “We know a significant number of people died before the WTCHP was set up; it’s likely to be in the hundreds. There are also probably hundreds of people outside the program who are sick and may have died.”

The WTCHP has certified 37,000 people as suffering from serious respiratory or digestive illnesses, cancer, or a combination. Most of those registered are from New York City and 82% are male.

Spring said: “There are health conditions covered in the program that will take years to develop and we don’t think the cancers we are seeing now is the end of it. It’s such an unprecedented disaster. It’s mind-boggling to think not just about the day but about the ripple effect on people’s health.”

The Manhattan borough president, Gale Brewer, told the Guardian she had “heard very high numbers” of people were at risk of dying from exposure to World Trade Center-related toxins.

“Many more than 3,000 or 4,000,” she said. “It’s very sad. I believe it will eclipse the number who died on 9/11 itself, because so many people were on the pile, or came to help, and so many people worked in the area. We are going to be dealing with this for years and years.”

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In 2014, Brewer wrote to New York governor Andrew Cuomo and New Jersey governor Chris Christie, asking them to approve a plan to build a monument to those sickened and killed since 9/11, to be installed near where the towers stood.

The area now hosts the National September 11 Memorial and Museum and is dominated by monuments built where each tower stood and engraved with the names of those who died in the atrocity.

Brewer is lobbying for a competition to design a separate monument for those who have been sickened. It will not have names, because of lack of clarity about cause of death in all cases and because it will also be designed to offer solace to those still living but sick, she said.

“It needs to be universal,” she said.

She has had no formal response from either Christie or Cuomo. But when she collared Cuomo at the Democratic convention in Philadelphia this summer, she said, he told her: “Sounds good.”

Brewer is hopeful of adding the monument before the 16th anniversary of 9/11.

Jerrold Nadler, the US congressman whose district includes the World Trade Center site, said of the post-9/11 health crisis: “It’s ghastly, it’s horrible, the people will die early and I feel very frustrated because it was preventable.”