When Senator Mitch McConnell of Kentucky, 81, wanted to quiet concerns about his health after two alarming on-camera episodes in which he appeared unable to speak or move, he turned to Dr. Brian P. Monahan.

Dr. Monahan, the low-profile and mild-mannered Navy doctor who has served for nearly 15 years as the on-site physician in the Capitol, quickly provided a clean bill of health for the longtime Republican leader. The brief and carefully worded statement matter-of-factly shot down several of the leading medical theories for what might be wrong with Mr. McConnell, including a seizure disorder, stroke and Parkinson’s disease.

The note drew criticism from some physicians and medical experts — including at least one who as a senator is among Dr. Monahan’s patients — and shone a spotlight on the unique and politically tricky job of the attending physician of Congress.

Dr. Monahan, whose job entails serving 535 members of Congress, the justices of the Supreme Court, staff aides and even tourists at the Capitol, has long sought to stay out of politics. But as a visibly diminished Mr. McConnell seeks to assert his continued control of his conference and shut down swirling concerns about his ability to lead, his case has thrust Dr. Monahan into the center of an ethical debate, raising questions about how he balances his medical duties as a physician with the political dimensions of his job.

“The ethicists sometimes call it the problem of dual loyalty,” said Dr. Arthur Caplan, a medical ethicist at N.Y.U. Langone. He compared the role of attending physician of Congress to that of a doctor on a professional sports teams. Each has obligations both to their individual patients and to their employers, organizations which rely on their patients remaining healthy enough to work or play, leading to potential conflicts of interest.

“You know the coaches and the owners want the athletes out there playing, but you also want to look out for their health,” Dr. Caplan added.

Several medical professionals who watched video of Mr. McConnell’s episodes have suggested that the Kentucky Republican, who had a serious fall in March that led to a concussion, was experiencing focal seizures or mini strokes, and took issue with Dr. Monahan’s assertion that there was no evidence of either. Some called the doctor’s suggestion that Mr. McConnell was simply suffering from dehydration particularly irresponsible.

“Medicine shouldn’t be politicized,” said Senator Rand Paul, Republican of Kentucky and an ophthalmologist. “And if you’re giving advice on what someone’s potential diagnosis is, really, it ought to be based on the facts. And what I can tell you is that having vacant spells of 30 seconds or more where you’re unresponsive is not a sign or a symptom of dehydration.”

“When you have misinformation put out there, like ‘just dehydration,’” Mr. Paul added, “it leads to further conjecture, well, maybe there’s something else we’re not telling.”

Dr. Monahan works directly for the congressional leaders. While lawmakers praise him as trustworthy and discreet, his office, whose taxpayer-funded budget is set by Congress, is extraordinarily averse to public scrutiny.

Keith Pray, Dr. Monahan’s chief of staff, said the physician’s office has no press person and the doctor “does not provide interviews/statements.” Dr. Monahan also did not reply to requests for an interview.

Former President Barack Obama appointed Dr. Monahan to be the attending physician of Congress in 2009. He had been selected for the post by the secretary of the Navy, making him the seventh person, and the seventh Navy doctor, to take up the position. Dr. Monahan, a rear admiral, is certified by the American Board of Internal Medicine in internal medicine, hematology and medical oncology, according to a biography on the Uniformed Services University website.

The House created the role in 1928, after one lawmaker died and two collapsed in a month, with hours passing in each case before a doctor could arrive at the Capitol. The Senate extended the House doctor’s jurisdiction to include that chamber two years later, leading to the establishment of the Office of the Attending Physician. The O.A.P. has since resided in a warren of blue-carpeted rooms located across from the speaker’s press office in a secluded hallway on the first floor of the Capitol.

Lawmakers who want additional primary care services from the attending physician must pay a fee. The O.A.P. is funded through the annual legislative branch appropriations bill; it received $4.2 million for fiscal year 2023.

Like any other doctor, Dr. Monahan is bound by federal medical privacy rules and the expectation of privacy between physician and patient. Still, members of Congress have often invoked the authority of the congressional physician to dispel rumors or allay concerns about their health status, as Mr. McConnell did twice in recent days.

“I do think at some points in time, he has to play politics, and I appreciate how tough that is, that he does want to be as neutral as possible,” said Republican Senator Roger Marshall of Kansas, an obstetrician-gynecologist. “I think he’s in a tough, tough position. But I don’t think he would ever do anything that he would say is not true in his heart.”

How lawmakers choose to use the attending physician’s medical advice often depends on the politics of the moment. After Senator John Fetterman, the Pennsylvania Democrat who had a life-threatening stroke last year, was hospitalized this year and faced questions about whether he was healthy enough to continue serving, his office announced that he was checking himself in to Walter Reed National Military Medical Center to receive treatment for clinical depression. Aides let it be known that Dr. Monahan had recommended the move after examining the senator.

Representative Jamie Raskin, a Democrat of Maryland who survived a battle with cancer this year with Dr. Monahan as his primary care physician, said the doctor “zealously guards the doctor-patient relationship.”

“If patients want to use the authority of the Capitol physician to lower the pressure on some medical situation, it has to be done through that letter,” Mr. Raskin said, referring to a statement of the kind Mr. McConnell released.

Such statements almost always proclaim the elected official to be in tiptop shape.

Two months after Senator Bernie Sanders, independent of Vermont, had a heart attack in 2019 in the thick of a presidential campaign, he released a lengthy letter from Dr. Monahan saying he was “in good health,” and had been “engaging vigorously in the rigors of your campaign, travel and other scheduled activities without any limitation.”

In 2012, as Representative Paul D. Ryan, Republican of Wisconsin, was making a vice-presidential run alongside Mitt Romney of Utah, Dr. Monahan wrote that Mr. Ryan regularly engaged in “vigorous aerobic and strength-building exercises,” ate a “heart healthy diet,” and did not smoke or drink much alcohol.

“The system is set up where it just says, ‘I’m clearing you to serve,’” Dr. Caplan, the medical ethicist, said of the Office of the Attending Physician. “That’s not transparent, and that isn’t the information that I think voters and the public deserve.”

But for the lawmakers who depend on Dr. Monahan, transparency is not seen as a virtue.

“He stands behind a wall of silence,” Mr. Raskin said. “Politicians can invoke their physician or show a letter from the physician. But he doesn’t thrust himself into the center of the public controversy by taking questions and so on.”

Yet he has not always been able to avoid controversy. While Dr. Monahan was widely trusted during the coronavirus pandemic, he also received criticism from leading Republicans for the stringent public health precautions instituted at the Capitol during the crisis, which the House speaker at the time, Representative Nancy Pelosi, made clear were put in place in consultation with him.

In July 2021, Ms. Pelosi reinstated a mask mandate at Dr. Monahan’s recommendation, amid fears of the Delta variant and uncertainty around how many members of Congress had been vaccinated. House Republicans, led by Representative Kevin McCarthy of California, then the minority leader, criticized Dr. Monahan’s advice as “inconsistent with the best available science.”

Representative Larry Bucshon, Republican of Indiana, soon introduced the “Office of Attending Physician Independence Act,” a measure that would make the attending physician a Senate-confirmed position with a 10-year term, and thus subject to stricter oversight by Congress. (The legislation went nowhere.)

“As a doctor, it appalls me to think doctors are put in a position to have to answer to political pressures, rather than set forth guidance based on facts and medical expertise,” Mr. Bucshon, a cardiothoracic surgeon, testified to the House Administration Committee in 2021.

Pressed by Republican members of the administration panel in March on whether he had faced any political pressure in preparing his coronavirus recommendations, Dr. Monahan said he had communicated regularly with leaders across both parties and been “subject to the full diversity of views.”

“Some would call it pressure,” he said then. “I would just call it opportunities to listen more closely.”