Yet the senator and the eye doctor have grown close and enjoy each other’s company, associates say. Melgen, a Dominican-born immigrant, sees the U.S.-born Menendez as the embodiment of American success and an important player on the national stage, and frequently refers to him as a “great man,” associates say. “Sal is sort of flattered to be with Menendez,” one person said.

Melgen’s attorney has said the doctor, proud of the friendship, is not worried about any investigation into the relationship. Moreover, the lawyer said, Melgen’s firm has a legal contract to provide port security that the Dominican government should enforce, and he said Melgen’s Medicare billing was justified.

Menendez speaks in adoring terms about Melgen and his wife. “We’ve developed a close relationship together,” he said, describing Melgen as “a very thoughtful guy.”

The two have spoken weekly over the past 20 years. Menendez has visited Melgen at his Dominican home more than two dozen times, according to a person familiar with their relationship.

In the interview Thursday, Menendez rejected the notion that his relationship with Melgen was problematic. Melgen’s requests often aligned with Menendez’s public policy aims, the senator said. Menendez pointed to his efforts on behalf of Melgen’s port security deal in the Dominican Republic, which called for operating X-ray scanners to screen cargo. This fit with the goal of fighting drugs and terrorism, the senator said.

Menendez’s friends and supporters often raise policy issues in social settings. And while he said he would usually prefer to be talking about sports or music rather than his work in Washington, the discussions “inevitably head in that direction.”

“It’s like the family member who’s a doctor and everybody starts asking them, ‘Oh, I have this twitch, I have this pain,’ or the family member who’s a stockbroker and [says], ‘Hey, you got any good tips for me?’ ” Menendez said.