Saying that his powers were too limited to rectify what he referred to as a “grave harm,” a federal judge on Monday dismissed a request from several families of 9/11 victims to sift through tons of debris at the Fresh Kills landfill to search for human remains from the attack on the World Trade Center.

The judge, Alvin K. Hellerstein of Federal District Court in Manhattan, had hinted strongly at an emotional hearing in February that he would deny the request, praising the city for undertaking the “herculean job of repairing the gaping hole in our society,” and saying that nothing — not even the upheaval of 1.8 million tons of landfill debris — would ever return the dead to their families.

In his ruling on Monday, which he said he was making reluctantly, Judge Hellerstein wrote: “Not every wrong can be addressed through the judicial process. The grave harm suffered by the plaintiffs in this case is undeniable. But the jurisdiction of a court is limited.”