President Biden plans to announce on Tuesday that his administration has approved more than one million claims from veterans injured by toxic exposures during their service, actions made possible by a new law he championed, officials said.

The president signed the Promise to Address Comprehensive Toxics, or PACT, Act, into law in the summer of 2022, with the goal of quickly getting benefits to veterans who had been suffering from a variety of maladies that did not qualify for treatment by the Department of Veterans Affairs.

“The president, I think, has believed that for too long, too many veterans who got sick, serving and fighting for our country, had to fight the V.A. for their care, too,” Denis McDonough, the veterans affairs secretary, said on Monday. He said Mr. Biden demanded that the V.A. “act quickly to be better, to do better.”

Mr. Biden is expected to travel to the Merrimack YMCA in New Hampshire on Tuesday for an event in which he will announce the milestone.

Officials told reporters on Monday that more than 888,000 veterans and their surviving family members are the recipients of about $5.7 billion in health benefits from the one million claims approved under the PACT Act since its passage.

That includes veterans suffering from cancer, allergic rhinitis, bronchial asthma, hypertension, sinusitis and other conditions, often related to the respiratory system. The law is aimed at providing support for veterans exposed to toxins, often from open burn pits that spewed them near where soldiers were living and working.