Corrected 2:20 p.m. | NEW YORK — One day ahead of the 20th anniversary of 9/11, Senate Majority Leader Charles E. Schumer said he would work to include more funding in the sweeping budget reconciliation bill for the health care needs of those who survived and responded to the attacks.

The House is already planning to include funding, and Schumer’s support makes it likely that if a bill comes together, it will be included.

“I am making a commitment here today that I will use everything in my power to get this in the Senate reconciliation bill as well,” the New York Democrat said. “And I believe we will succeed in that effort.”

Schumer joined Democratic Reps. Carolyn B. Maloney and Jerrold Nadler, Democratic Sen. Kirsten Gillibrand and Rep. Andrew Garbarino, R-N.Y., as well as advocates for the funding at an event here on the Upper East Side on Friday morning.

“As we mark 20 years since that fateful day in 2001, we must remember that 9/11 isn’t just in the past,” Maloney said. “It is something that these responders, survivors and their families are living with each and every day as they deal with cancer, respiratory disease and mental health concern.”

​Maloney, who led Friday morning’s event outside the medical school at Mount Sinai hospital, was one of several lawmakers to remind attendees about the erroneous information that the government provided about the air quality at Ground Zero in the immediate aftermath of Sept. 11.

“The toxic lie that our government told them,” said Maloney, wearing a familiar New York City Fire Department firefighter’s coat, a version of which she has worn countless times during debates over first-responder assistance on Capitol Hill.

Gillibrand recalled seeing the billowing smoke and knowing it was toxic.

“The EPA at the time lied ​to ​them under George Bush and said the air was safe. The air was not safe. It was crushed metal and glass and electronics and building materials​.​ It was a toxic sludge that is now affecting people, and people are losing their lives,​” ​Gillibrand said.

The funding the lawmakers says is needed would provide more funding for the 9/11 World Trade Center Health Program, which was made permanent in 2015. It covers qualified medical expenses for first-responders and survivors of the terror attacks 20 years ago. Its provisions apply not only to those affected in lower Manhattan but also in Shanksville, Pa., and at the Pentagon.

The problem outlined by the New York delegation members and supporters Friday? The law calls for the health care program to receive an annual funding adjustment based on the rate of inflation. But the costs associated with 9/11-related cancers and other conditions are going to outpace that.

Garbarino, who succeeded former lead GOP sponsor Rep. Peter T. King in a Long Island-based seat, said he never anticipated that the funding issue would still be a problem when he arrived in Congress.

“People don’t realize that people are still getting sick,” Garbarino said, adding that he has friends and family members who are still developing illnesses.

New Jersey Democratic Rep. Frank Pallone Jr., the Energy and Commerce chairman, has proposed to include $2.86 billion in funding for the shortfall, as well as to cover the city of New York’s 10 percent match, in his committee’s portion of the Democrats’ budget reconciliation package.

The Pallone measure is scheduled to be marked up on Monday.

“As we prepare to remember the 20th anniversary of the 9/11 terrorist attacks on our country, we must renew our commitment to never forget the sacrifices first responders made on that day and the survivors who continue to endure the physical and emotional trauma. This funding is essential to ensuring that we fulfill our obligation to the individuals who require medical care,” Pallone said in a statement.

A bipartisan letter sent to House leadership and Energy and Commerce leadership on Sept. 3, signed by 28 House members and led by Maloney and Nadler, said that beneficiaries of the 9/11 fund for monitoring or treatment reside in 434 of the country’s congressional districts.

Nonetheless, the health funding has always faced objections, in part because of the ever-increasing and unknown costs.

Schumer recalled past Senate battles, including when the late Tom Coburn, R-Okla., initially objected to the legislation, leading to an agreement for a five-year authorization in 2010. But, he said, the timing was somewhat fortuitous.

Garbarino said after the event that he hoped the Democrats wouldn’t rely on getting the reconciliation deal through to pass the bipartisan health funding.

“They should bring this bill up tomorrow, and I think it would pass,” Garbarino said of a stand-alone version. “In three weeks — I’ve gotten Republicans from eight states, and they were on vacation — so when we go back into the session on the 20th of September, I think I’ll even get more. They should bring this bill up right away.”

This report was corrected to reflect the 2015 permanent authorization of the 9/11 World Trade Center Health Program.