WASHINGTON, Oct. 22  -- U.S. President Barack Obama said Wednesday he is "cautiously optimistic" about the Ebola situation in the United States, as his government announced a new program that will actively monitor for 21 days every person coming from West African nations hard hit by the deadly virus.

"The public health infrastructure and systems that we are now putting in place across the board around the country should give the American people confidence that we're going to be in a position to deal with any additional cases of Ebola," Obama said after meeting his new Ebola response coordinator Ron Klain and other officials in the Oval Office.

Obama mentioned "a number of things" that made him "cautiously optimistic," including the clearance of dozens of persons who had initial interaction with the now deceased Thomas Eric Duncan, the first person diagnosed with Ebola on U.S. soil.

He reported that two nurses from the Texas Presbyterian Hospital who were infected while treating Duncan "seem to be doing better" and that the spirits of coworkers of the two infected nurses whom he spoke to earlier in the day "were good."

Obama also said he is "very happy" about the news that two American patients, who got Ebola in West Africa but were brought back for treatment, have been released from the hospital this week.

Internationally, he spoke of a declaration by the World Health Organization that Nigeria and Senegal are now Ebola-free, saying that "it gives you some sense that when it's caught early and where the public health infrastructure operates effectively, this outbreak can be stopped."

He reassured Americans that the prospect of an outbreak in the U.S. is "extremely low."