Dr. Aquino, 54, of Glen Head, N.Y., told Judge Rakoff that in return for the payments, he understood Mr. Kruger, a Brooklyn Democrat, “would take official actions in an effort — a failed effort — to keep Parkway Hospital open.”

“It was your intent to bribe him?” Judge Rakoff asked at one point.

“Yes, Your Honor,” Dr. Aquino replied.

Judge Rakoff told Dr. Aquino he could face a sentence of five years in prison for the one count.

In its agreement with Dr. Aquino, the government said that it would write a letter “to appropriate medical licensing boards” describing the facts and circumstances of his case, as well as “the defendant’s prior cooperation on another matter.” The document does not elaborate, and neither prosecutors nor Dr. Aquino’s lawyer would say what the matter involved.

Dr. Aquino’s lawyer, Peter B. Pope, said after the proceeding, “This is a situation where the doctor wants to accept responsibility for his actions and move on with his life and try to do good for people, the way he has in the past. He’s been a doctor a long time.”

Mr. Pope said that his client had practiced in emergency rooms and later managed them.

Preet Bharara, the United States attorney in Manhattan, said Tuesday that Dr. Aquino had been “all too willing to make sure a bribe was paid to preserve his job” as a hospital chief executive. “Like others in this case, he chose to fight his battle with money under the table rather than to play by the rules,” Mr. Bharara added.