|Texas Health Presbyterian Hospital says it was prepared for a potential case|
Five children in Texas who came into contact with a man infected with Ebola are being monitored at home.
At a news conference at Texas Health Presbyterian Hospital in Dallas, the state's governor Rick Perry said parents were concerned but he allayed fears of contagion.
Officials said they are monitoring up to another dozen people who may have come into contact with the man.
Thomas Eric Duncan is thought to have contracted the virus in Liberia.
The Liberian national came to the US nearly two weeks ago to visit relatives and he is the first man to be diagnosed with Ebola while in the US.
Mr Duncan is now in a serious condition, a spokeswoman for the hospital said.
A nurse had asked him on his first visit to the hospital when he felt ill if he had been in an area affected by the Ebola outbreak.
He told them he had been to Liberia but the "information was not fully communicated throughout the whole team", according to hospital officials.
Mr Duncan was then sent home with antibiotics - a decision hospital bosses have described as a matter of "regret" - but he was admitted when he returned two days later.
Allaying fears that Mr Duncan might have infected others, Mr Perry said his state had the medical infrastructure to prevent an outbreak.
"There are few places in the world better equipped to meet the challenge that is posed in this case."
More than 3,000 people have already died of Ebola in West Africa and a small number of US aid workers have recovered after being flown to the US.
Meanwhile, in Liberia a government spokesman said the man showed no symptoms or fever as he was screened before departing the country.
"What this incident demonstrates is the clear international dimension of this Ebola crisis," Lewis Brown, the country's information minister, said in a statement.