Texas Governor Rick Perry says health officials are keeping watch on as many as 18 people who came in contact with Thomas Eric Duncan, the first patient to be diagnosed with Ebola in the United States.
Ambulance workers who brought Duncan to the hospital have tested negative.
Those with whom he had contact since arriving in the United States on September 20 will be monitored for at least 21 days. But officials say no other cases are suspected.
Jennifer Fisher, New York University Langone Medical Center, said: "Every hospital in the United States needs to be prepared. It is possible that there will be more cases in the U.S., but again, there is no risk to the general public."
Duncan, who arrived in the United States from Liberia, is in isolation in a Dallas hospital. He was listed as serious but stable condition Wednesday.
There is no specific treatment, but an American doctor diagnosed with the virus was found to be Ebola-free after taking an experimental drug in August.