Thomas Eric Duncan, who caught the virus in his native Liberia, is being treated at a Dallas hospital in isolation.
Earlier it emerged that the flat where he lived is being cleaned by hazardous materials specialists and its remaining four occupants moved to a private home.
Some 3,431 people have died in West Africa in the worst Ebola outbreak yet.
On October 3, a senior US military figure said the US could deploy as many as 4,000 troops to the region to help contain the outbreak, which has hit hardest in West African four nations.
While Thomas Eric Duncan is the first person to be diagnosed within the US, three American aid workers and a photojournalist contracted the virus in Liberia.
Texas Health Presbyterian Hospital issued a six-word statement about Thomas Eric Duncan on October 4, saying only that: “Mr. Duncan is in critical condition.”
Earlier his condition had been described as serious but stable.
Ebola spreads through contact with the bodily fluids of someone who has the virus and the only way to stop an outbreak is to isolate those who are infected.
There have been nearly 7,500 confirmed infections worldwide, with officials saying the figure is likely to be much higher in reality.
Guinea, Sierra Leone and Liberia have been hardest hit.
Celebrations in West Africa for the Muslim festival of Eid al-Adha are being badly affected by the Ebola outbreak, with many public places deserted this weekend.
Meanwhile, a French nurse who got the virus in Liberia has recovered after having experimental treatment in Paris, it has emerged.
A Senegalese medical expert who was infected in Sierra Leone has also been discharged from a hospital in the German city of Hamburg.
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