Craig Spencer crisscrossed New York City in the days after he returned from treating Ebola patients in West Africa — riding the subway, going for a three-mile run, grabbing coffee on the High Line, bowling in Brooklyn.

And while the 33-year-old doctor notified authorities when he developed a fever and was quickly isolated at Bellevue Hospital Center, his own Ebola diagnosis prompted the governors of New York and New Jersey on Friday to impose a mandatory 21-day quarantine for medical workers returning from the countries hit hardest by the epidemic. Illinois later in the day imposed similar restrictions.

That action all but overshadowed the day’s good news: In Washington, a smiling Dallas nurse named Nina Pham hugged President Obama in the Oval Office after being declared Ebola-free by doctors and leaving the National Institutes of Health. And in New York, physicians said Spencer remained in stable condition, while officials fanned out to track down anyone he might have encountered in recent days.

The new quarantine rules, instituted late Friday by New York Gov. Andrew M. Cuomo (D) and New Jersey Gov. Chris Christie (R), came amid a deepening debate across the country over whether federal restrictions need to be tightened for anyone arriving in the United States from the Ebola-stricken countries of West Africa.

Those in favor of strict quarantines argue that the current federal requirement — that travelers without symptoms take their temperatures regularly and report them to state and local health departments — are too lax and that it’s foolish to allow people with potential exposure to Ebola to move freely throughout society.

But those who oppose automatic quarantines insist that proper self-monitoring removes almost any likelihood of transmission, given that Ebola typically is contagious only after symptoms appear. They say that requiring a three-week quarantine would deter some aid workers from traveling to West Africa to fight the unprecedented epidemic. Hundreds of health-care workers have been cycling in and out of Africa to care for Ebola patients.

The Obama administration said it was weighing the dilemma.

“We do want to ensure that whatever policies we put in place takes as the first priority the protection of the American public,” White House press secretary Josh Earnest told reporters Friday. “But at the same time, we don’t want to overly burden those individuals who are going to great lengths to try to serve their fellow man and stop this outbreak at the source, which ultimately is in the best interests of the American people.”

Some experts worry that it is already happening.

“For everybody who is professionally trying to go to the three epidemic countries, the situation has become more difficult with each passing day and each Ebola case — or alleged Ebola case — named in the United States,” said Laurie Garrett, a senior fellow for global health at the Council on Foreign Relations, who says returning health workers should voluntarily isolate themselves upon return.

In statistics released Saturday by the World Health Organization, more than 10,000 Ebola cases had been reported in eight countries as of Thursday. Deaths number nearly 5,000.

Mark Rothstein, a bioethics professor at the University of Louisville School of Medicine, said the federal government could try to strike a compromise, such as recommending that health-care workers returning from West Africa adhere to a mandatory 10-day quarantine followed by self-monitoring.

The lack of consensus among federal and state governments, as well as among international aid groups, on how to deal with volunteers returning from Ebola-ravaged countries underscored the confusion, fear and political pressure caused by the handful of Ebola cases that have surfaced in the United States.

But even groups working on the front lines of the crisis disagree on whether returning volunteers should face mandatory isolation for weeks, away from their friends and family, if they are healthy and follow self-monitoring guidelines.

Doctors Without Borders, which employed Spencer in Guinea and has led the effort to combat Ebola in West Africa, said this week that quarantining is neither warranted nor recommended in the absence of symptoms and that as long as a returning staffer remains healthy, “normal life can proceed.” The group has specific guidelines for the returning aid workers, including checking their temperatures twice daily and contacting the organization immediately if symptoms develop — something Spencer did.

Until this week, the group said in a statement, “out of more than 700 expatriate staff deployed so far to West Africa, no [Doctors Without Borders] staff person has developed confirmed Ebola symptoms after returning to their home country.”

Meanwhile, the North Carolina-based international relief group Samaritan’s Purse, which has nearly two dozen expatriate staffers working in Liberia, has chosen to go beyond CDC recommendations.

“We just didn’t have confidence in them, quite frankly,” Samaritan’s Purse Vice President Ken Isaacs said of the CDC guidelines. “We felt more strict protocols were in order, so we created our own.”

The relief group began requiring all returning staff to stay isolated for 21 days, away from family members. The organization houses workers within an hour’s drive of medical facilities, such as Emory University or the NIH, which are equipped to handle Ebola patients, in case someone gets sick. The workers, who are paid their normal salaries, are not allowed to take public transit or touch anyone, and they must take their temperature multiple times a day.

“That’s just a part of the deal, and they have accepted that,” said Isaacs, who acknowledges that the requirements make it potentially more difficult to recruit volunteers to work in West Africa. “We’ve never felt comfortable that just coming back and letting people go about life as normal and take their temp two times a day was sufficient.”

A health-care worker who flew into Newark Liberty International Airport on Friday and had no symptoms at the time would still be quarantined because she had treated Ebola patients in West Africa, Christie said.

The New Jersey Department of Health announced Friday evening that the unidentified woman had “developed a fever and is now in isolation and being evaluated at University Hospital in Newark.” On Saturday, AP reported, the woman had tested negative for Ebola in a preliminary evaluation but remained in isolation.

New Yorkers themselves disagreed about what kind of restrictions should be imposed on medical workers coming back from West Africa.

“It seems a quarantine would be unnecessary,” said John Ard, an anesthesiologist affiliated with Bellevue and NYU Langone Medical Center. “We should stick with the science and avoid hysterical overreaction.”

But Tom Sullivan, who was working on a construction project a block from Bellevue, said quarantines make sense for returning health workers. “You’re working with diseased people. That’s common sense. It doesn’t take a rocket scientist.”

Spencer, a doctor at New York-Presbyterian/Columbia University Medical Center, had gone to Guinea in September to work with Doctors Without Borders. He returned last week after a stop in Brussels and had been healthy until he began feeling sluggish on Tuesday. He was receiving fluid and electrolytes and remains in good enough shape to talk on the phone and help disease detectives from the health department retrace his steps this week, authorities said.

Officials said in recent days, after Spencer began feeling fatigued but before he developed a fever, Spencer went running, visited a bowling alley in Williamsburg, rode three New York subway lines and used an Uber car. His fiancee and two other friends have been placed in quarantine, but officials have not identified any other high-risk contacts and continued to urge calm among city residents.

“New Yorkers who had not been exposed to an infected person’s bodily fluids are simply not at risk,” New York Mayor Bill de Blasio (D) said Friday. “There is no reason for New Yorkers to change their daily routine in any way.”

As Spencer began his fight against the deadly disease Friday, Pham, the first nurse diagnosed with Ebola in the United States, walked out of the NIH. Pham, 26, had become infected while treating an Ebola patient in Dallas.

“I feel fortunate and blessed to be standing here today,” she said. “Throughout this ordeal, I have put my trust in God and my medical team. I am on my way back to recovery, even as I reflect on how many others have not been so fortunate.”

Pham spoke of returning to Texas and to a normal life with her dog, Bentley, the much-photographed King Charles spaniel who was quarantined after Pham’s diagnosis but has tested negative for Ebola.

Amy Ellis Nutt in New York, Juliet Eilperin, Lenny M. Bernstein and Dan Morse contributed to this report.