WASHINGTON — The House on Friday approved legislation to replenish a depleted federal fund to compensate emergency workers and others who became ill as a result of their work in the ruins of the World Trade Center in Lower Manhattan, extending it for the lifetime of those who were at Sept. 11’s ground zero.

The bill, passed by a lopsided bipartisan 402-12 vote, would authorize $10.2 billion for the September 11th Victim Compensation Fund. It comes in the face of a large uptick in medical claims from people who worked on “the pile,” as the steaming heap of steel rubble was often called by those who labored there in the months after the attack in 2001. Many of them have since become gravely sick with cancer and other ailments.

Representative Carolyn B. Maloney, Democrat of New York, who has led the charge to replenish the fund, said the bill fulfilled “a moral obligation” Congress has to the Sept. 11 emergency workers, who rushed to the rubble immediately after the attacks, and others who worked there in the months that followed. The cause was championed by the comedian Jon Stewart and brought to an emotional peak by the death two weeks ago of Luis G. Alvarez, a former New York City detective and advocate for the emergency workers.

“It’s the least we can do as a grateful nation,” Ms. Maloney said. “They were there for us; we have to be there for them, and we have a double moral responsibility. Not only were they the veterans of the war on terror, they were told by their government that the site was safe, when it was not.”