The United States’ months-long effort to stop the deadly Ebola outbreak is reaching a “pivot point,” but Americans should expect more domestic cases, White House Ebola czar Ron Klain said Sunday.

“We will see (cases) from time to time,” Klain told CBS’ “Face the Nation.” “There’s still work to be done in Sierra Leone and Guinea. But we’re nearing a pivot point.”

Klain was appointed to the post in October by President Obama to lead the U.S. response to Ebola, days after the first death on U.S. soil as a result of the disease.

Thomas Eric Duncan died October 8 at Texas Health Presbyterian Hospital, in Dallas, after returning for Liberia, one of the countries in West Africa where Ebola has killed roughly 7,600 people this year.

Duncan went to the hospital days earlier with Ebola-like symptoms, but was treated and released. The situation combined with two of Duncan’s nurses becoming infected raised widespread concerns about lapses in protocol and the potential for a U.S. outbreak.

Among the roughly 19,340 cases recently confirmed by the World Health Organization, Sierra Leone has the most with 8,939, followed by Liberia at 7,830 and Guinea with 2,571.

In September, Obama assigned 3,000 U.S. military members to West Africa to help with the outbreak, providing medical and logistical support for the region’s overwhelmed health care systems.

Klain, a long-time Democratic operative and former chief of staff to Vice President Biden, also told CBS that the number of cases in that region is now at five to 10 a day, compared to 50 to 100 daily.

“But this won’t be over until we get to zero,” he said.

The most recent case of Ebola being diagnosed in the U.S. occurred on October 23 when the New York City Department of Health and Mental Hygiene reported one in a medical aid worker who had returned to the city from Guinea, where he had served with Doctors Without Borders.

The patient recovered and was discharged from Bellevue Hospital Center on Nov. 11, according to the Centers for Disease Control and Prevention.

Klain called the CDC’s mishandling last week of an Ebola sample “unacceptable” but said the technician involved has so far shown no signs of infection.

He called the use of an Ebola blood test at the “point of care” a “very significant step” in the fight to stop the outbreak in West Africa.

Klain said the Ebola vaccine recently approved by the Food and Drug Administration is scheduled for release in three to four weeks and will help “tens of thousands of people.”