President Barack Obama says Americans should not to give in to "hysteria" about the spread of the Ebola virus despite cases being diagnosed in the United States.

He made the remarks while emphasizing his opposition to a proposed travel bans on the West African countries where the virus outbreak has reached epidemic proportions.

What is happening in the United States is not in any sense an outbreak, he said in his weekly address carried on radio and online.

"We have to be guided by the science," the president said. "We're a nation of more than 300 million people. To date, we've seen three cases."

The president's address follows his appointment of Ron Klain, a former White House adviser, as an "Ebola czar" to head America's response to the virus, amid growing concerns the disease might spread beyond the three cases confirmed in Dallas.

Two health care workers who cared for an Ebola patient who later died in a Dallas hospital are currently being treated for the disease, and their condition is said to be improving.

Guarding against hysteria should be a concern for all Americans, the president said.

"Meeting a public health challenge like this isn't just a job for government," he said. "All of us -- citizens, leaders, the media -- have a responsibility and a role to play. This is a serious disease, but we can't give in to hysteria or fear because that only makes it harder to get people the accurate information they need."

Health experts, who say the disease is effectively contained in the U.S., have criticized proposals for a travel ban.

A travel ban to and from Africa could keep necessary medical supplies and healthcare workers from being sent to the hardest-hit countries of Liberia, Guinea and Sierra Leone, they point out.

If such aid is not able to reach those countries there is a risk of the disease spreading more widely in Africa, which would in turn increase the level of risk to the United States and the rest of the world, they say.

President Obama echoed those concerns in his address.

"We can't just cut ourselves off from West Africa," he said. "Trying to seal off an entire region of the world -- if that were even possible -- could actually make the situation worse."

Numerous Republican lawmakers have called for a ban, along with some Democrats.

House Speaker John Boehner, R-Ohio, says he also favors a travel ban.