Sylvia Burwell, Secretary of Health and Human Services, left, and Dr. Thomas Frieden, Director of the Centers for Disease Control and Prevention, far right, listen as President Barack Obama speaks to the media about the government’s Ebola response, in the Oval Office of the White House Thursday, Oct. 16, 2014, in Washington. (AP Photo/Jacquelyn Martin)

President Obama said Thursday night he would consider appointing an Ebola czar to coordinate the federal government's efforts to combat the deadly virus.

Speaking after meeting with some of his top advisers in the Oval Office, the president said that at some point in the future it might make sense to have one person coordinating the federal response.

"It may make sense for us to have one person in part just so that after this initial surge of activity we can have a more regular process," he said, "just to make sure that we're crossing all the t's and dotting all the i's going forward. "

Obama emphasized that he and his deputies -- who met for nearly two hours Thursday night -- were working hard to keep the public safe.

"We are taking this very seriously at the highest levels, starting with me," he said, noting at one point, “I understand people are scared.”

Republicans have pressed the president for weeks to name one person to direct efforts to contain the disease. The White House has resisted the proposal, though press secretary Josh Earnest has said repeatedly the administration might adjust its response as needed.

Lisa Monaco, who serves as assistant to the president for homeland security and counterterrorism, is overseeing the interagency response to the disease. In addition to Monaco, the State Department has appointed former U.S. ambassador to India Nancy Powell to coordinate the diplomatic response to the outbreak. Major General Darryl Williams, in his capacity as Commander of U.S. Army Africa and Operation United Assistance, oversees the military effort to contain the outbreak in West Africa.

In a statement Thursday night, Sen. John Cornyn (R-Tex.) said the White House “has done little over the past few weeks to inspire the confidence of Texans and the time for the administration to act is now."

"The president should immediately designate an experienced, proven leader to coordinate a national response involving local, state and federal agencies to contain Ebola in the United States, including considering temporary restrictions on travel from impacted West African nations,” Cornyn said.

While the president expressed some willingness to accept the idea of an Ebola czar, he said he was still opposed to imposing a travel ban on passengers coming from the three countries most impacted by Ebola.

“I don't have a philosophical objection necessarily to a travel ban if that is the thing that is going to keep the American people safe, Obama said, but he said some travelers might try to circumvent the system and “we may end up getting less information about who has the disease."

“It is currently the judgment of all those who have been involved that a flat-out travel ban is not the best way to go,” he added.

White House press secretary Josh Earnest was asked Thursday if President Obama was angry that another health-care worker was diagnosed with Ebola in the U.S. Earnest responded saying that some aspects of the response "have fallen short" of Obama's expectations. (AP)