President Obama said Monday the U.S. government would increase passenger screenings in the United States and Africa to detect the Ebola virus, even as he resisted calls to impose a ban on those traveling from the three countries most affected by the outbreak.

Neither the president nor White House officials elaborated on exactly what those new screenings would entail. At the moment, passengers leaving the three nations most affected by the virus — Liberia, Guinea and Sierra Leone — are screened for symptoms at the airport before departing.

“The ability of people who are infected who could carry that across borders is something that we have to take extremely seriously,” Obama said Monday afternoon after a meeting with top advisers to discuss Ebola.

Obama spoke as Thomas Eric Duncan, as a Liberian man stricken with Ebola, remained in critical condition in a Texas hospital. And his remarks came shortly after a nurse in Madrid became the first person known to have contracted the virus outside of Africa. The nurse was caring for an Ebola-infected priest who had flown from Sierra Leone to Spain last month and subsequently died, according to Ana Mato, the Spanish health minister.

In his remarks Monday, Obama was sharply critical of countries that he said have not responded aggressively enough to the epidemic, which has killed more than 3,400 people and infected double that number. “Countries that think that they can sit on the sidelines and just let the United States do it, that will result in a less effective response, a less speedy response, and that means that people die,” he said.

The new screening possibilities being considered by the administration include taking the temperature of travelers from affected countries upon their arrival at major U.S. airports and more-closely tracking travel histories for international travelers arriving in the United States, said a federal official familiar with the discussions who spoke on the condition of anonymity because plans have not been finalized.

Obama emphasized that the country was prepared to contain Ebola, saying that he felt the odds of an epidemic in the United States “are extraordinarily low.”

“In recent months we’ve had thousands of travelers arriving here from West Africa,” he said, “and so far only one case of Ebola has been diagnosed in the United States, and that’s the patient in Dallas.”

Several Republicans on Monday called for heightened screenings or complete travel bans. Sen. Ted Cruz (R-Tex.) wrote a letter to the Federal Aviation Administration pointing out that the holiday season is nearing and asked whether the agency is planning to limit or suspend air travel to the Ebola-stricken countries. Gov. Rick Perry (R) of Texas was among those advocating “enhanced screening procedures” for people arriving in the country.

U.S. airlines said Monday they would meet with federal authorities to discuss ways to provide another layer of protection for their passengers.

Despite the measures under consideration, there does not appear to be a foolproof way to prevent people infected with Ebola from flying into the country. During two previous public-health panics — the swine-flu pandemic in 2009 and the outbreak of severe acute respiratory syndrome, or SARS, in 2002 and 2003 — flight crews were required to radio ahead whenever a passenger fell ill.

There are no direct flights by U.S. carriers from Sierra Leone, Guinea or Liberia. The vast majority of travelers from Africa to the United States fly through hub cities in Europe. Duncan flew from his native country to Brussels, where he boarded a flight to Washington Dulles International Airport, changed planes and continued on to Dallas.

The Ebola outbreak in West Africa has reached the United States, as officials confirmed one case in Dallas. Here's how U.S. health officials plan to stop the virus. (Gillian Brockell/The Washington Post)

If a passenger books travel on a single ticket — such as from Liberia to Brussels to the United States — tracking by U.S. Customs and Boarder Protection will reveal that the travel originated in Liberia. But information about a passenger who buys two tickets — Liberia to Brussels, and then Brussels to the United States — will not show up the same way in the agency’s data scan.

The U.S. Centers for Disease Control and Prevention maintains full-time offices at Dulles and other major U.S. destinations for international flights, and there are quarantine stations at major airports across the country.

A spokesman for the Metropolitan Washington Airports Authority, which manages Reagan National Airport and Dulles, said there have been only informal conversations regarding procedures in the event of a passenger suspected of having Ebola.

“As this has developed, it’s on the forefront of people’s minds,” said Christopher Paolino, a spokesman for the authority. “Everyone wants to make sure we are prepared.”

The FAA has the power to restrict flights by U.S. carriers and, working with the CDC and the White House, could revoke the right of specified foreign carriers to land in the United States. In a statement Monday, the agency noted that the World Health Organization and the CDC have not recommended tighter travel restrictions to or from the afflicted countries.

The White House was clear Monday that it has no plans to ban travelers from West Africa. “A travel ban is something that we’re not currently considering,” White House press secretary Josh Earnest said.

Public health officials have warned that a complete travel ban would cause economic harm, hinder the delivery of food and supplies and even limit the ability of doctors, nurses and humanitarian workers to travel into those areas.

Thomas Frieden, director of the CDC, said Sunday that the agency has increased exit screenings at airports in the Ebola-riddled countries, using a combination of thermometers, questionnaires and “visual inspection” of travelers.

This screening has stopped 77 people from boarding planes, including 17 last month, he said. However, Duncan was able to make his way into the United States simply by filling out a questionnaire saying he had not had contact with anyone infected with Ebola. When Duncan left Liberia, he had no fever and had no symptoms associated with the virus.

Meanwhile, the Dallas hospital treating Duncan said Monday that over the weekend he began receiving an experimental treatment for the deadly disease. Known as brincidofovir, the antiviral drug is produced by Chimerix, a North Carolina-based biotechnology firm.

The company said it has received permission to offer the drug to Ebola patients from the Food and Drug Administration, which must sign off on the experimental use of unapproved drugs. There currently are no approved treatments or vaccines for Ebola.

Duncan, who was diagnosed last week, joins a handful of other Ebola patients who have received experimental drugs during the course of the outbreak. Two U.S. missionaries infected this summer while working in West Africa were given doses of another unapproved drug, known as ZMapp, but the limited supplies of that drug were soon exhausted. An experimental medicine from a Canadian company, Tekmira, was given to another American doctor who was flown to Nebraska from West Africa for treatment.

Thomas Geisbert, a professor at the University of Texas Medical Branch at Galveston who has researched the Ebola virus for decades, said that no matter what happens with Duncan, it will be difficult to know what role the experimental drug played, because it was given so long after Duncan became ill.

“It may have been given so late that it doesn’t make a difference either way,” he said.

No one else who had contact with Duncan has shown any symptoms of Ebola, authorities said Monday.

The Dallas County prosecutor is considering whether to file criminal charges against Duncan.

“We are looking at whether he intentionally and knowingly exposed the public to the virus,” Debbie Denmon, a spokeswoman for the prosecutor’s office, said Monday. “It’s the issue of holding someone accountable, that you can’t just get on an airplane and lie on a travel document and get to the United States.”

Dallas Mayor Mike Rawlings and county officials said Monday they met with Louise Troh, the girlfriend of Duncan, who is in isolation at an undisclosed location with her 13-year-old son, as well as Duncan’s cousin and a 20-year-old man.

“We take temperatures twice a day. So far we have zero symptoms,” Rawlings said. “We will have fingers crossed and hands folded in prayer because this is an important week.”

Ashley Halsey III, Lori Aratani, Elahe Izadi, Juliet Eilperin and Sean Sullivan in Washington and DeNeen Brown in Dallas contributed to this report.