The first diagnosed case of Ebola in the United States, along with concerns that others might have been exposed, have spurred calls for the Obama administration to at least consider more severe measures to contain the virus – including blocking flights from Ebola-stricken countries.

Louisiana Gov. Bobby Jindal on Friday became the latest to make that demand.

“We should stop accepting flights from countries that are Ebola stricken,” the Republican governor said in a written statement. “Even countries in Africa have cut back on or stopped accepting flights from countries with Ebola outbreaks.”

So far, the administration is resisting the push. White House Press Secretary Josh Earnest said Friday there is no consideration of a travel ban right now, voicing confidence in safety procedures currently in place. 

At a White House press briefing, counterterrorism adviser Lisa Monaco said the most important step is to control the epidemic "at its source" and prevent people who may be ill from leaving West Africa. She said "dozens and dozens" of people already have been stopped through this kind of screening, though U.S. officials are "constantly going to evaluate" what measures to employ. 

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She argued that a travel ban would "actually impede the response" by slowing the ability of the U.S. and others to get assets to the region.

Centers for Disease Control and Prevention head Tom Frieden made a similar argument in an interview with Fox News. “I wish we could get to zero risk by sealing off the border, but we can't,” he said. "Other people who have a right to return or a visa to enter may come back. People will go to third countries and come from there. So sealing them off, first off won't work. Second off, it will backfire.” 

But Jindal said the argument that shutting down flights would be counterproductive “defies logic.”

“How exactly would stopping the entry of people potentially carrying the Ebola virus be counterproductive? This seems to be an obvious step to protect public health in the United States,” Jindal said.

The first case of Ebola in the United States was diagnosed in Dallas on Tuesday. While no cases have been diagnosed in Louisiana, Jindal said his state was prepared in the event it does happen.

In North Carolina, state House speaker and GOP Senate candidate Thom Tillis also has been vocal in calling for a travel ban. And in Texas, GOP Sen. John Cornyn fired off a letter to the head of U.S. Customs and Border Protection on Friday seeking more information on what screening processes are being used for incoming passengers.

Texas GOP Sen. Ted Cruz, too, wrote to Federal Aviation Administration chief Michael Huerta asking what the agency was doing to prevent the virus from spreading. Cruz asked whether the FAA has plans to “limit or suspend air travel to countries that have experienced a significant Ebola outbreak.”

The Federal Aviation Administration can order a suspension of flights to and from an area where public safety issues are a factor. In July, the FAA ordered a suspension of all flights to and from Israel’s main airport after rocket fire from Gaza. A senior GOP Senate aide, referencing that incident, told FoxNews.com that “it is a precedent that when issues of public safety are concerned, the president can ground air travel.”

The aide also pointed to the Immigration and Nationality Act in arguing the government has broad power to decide whether non-citizens are allowed on U.S. soil.

Section 212 of the law says “any alien” can be denied “visas or admission” into the United States if they are determined to “have a communicable disease of public health significance.”

The outbreak so far has been concentrated in West African nations like Nigeria and Sierra Leone, which saw 765 new cases last week alone, according to the Save the Children charity, which dispatched volunteers to help with the crisis.

“It’s like a powder keg,” the Senate aide said of the virus. “This is not a case where you have the luxury of erring on the side of permissiveness.”

As for dealing with U.S. citizens, aside from restricting flights, the U.S. government does have the power to quarantine people, even "well persons who may have been exposed" to a communicable disease. Quarantine orders are issued by the president. 

While many national health officials acknowledge the danger in the Ebola crisis, they continue to hammer the message that travel hubs like Chicago’s O’Hare International Airport and America’s borders in general are being closely monitored.

"We regularly communicate with local emergency responders and U.S. Customs and Border Protection officials to stay on top of any exposure," Christine Pearson, a spokeswoman for the CDC, said in a statement.

Pearson said that since Ebola has started to spread to western countries, the CDC has been providing more training and drafting new protocols for flight crews, emergency responders and U.S. Customs officers.

Frieden and Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases at the National Institutes of Health, are scheduled to testify before a House panel on Oct. 16.

“From the decisions of the Centers for Disease Control and Prevention to airline passenger screening procedures by Customs and Border Patrol, our goal is to ensure every step necessary is being taken to contain and prevent the spread of this deadly disease and ensure health and safety of all Americans,” Rep. Tim Murphy, R-Pa., said in a written statement Friday about the hearing. 

Fauci, who spoke at the same press briefing as Monaco on Friday, acknowledged "missteps" in the handling of the Dallas patient but claimed the system is working. He called an outbreak in the United States "extraordinarily unlikely." 

With the Dallas case triggering speculation about other possible cases, Monaco did not discount the possibility that more could be infected. 

"It is entirely possible we will see another case." But she said officials are "very confident" they can stop this. 

"The United States is prepared to deal with this crisis," Monaco assured. "We know how to do this, and we will do it again."