WASHINGTON (AFP) - The Texas health-care worker who became infected with Ebola while caring for a Liberian man who died of the illness said on Tuesday that she is doing well, according to a hospital statement.

"I'm doing well and want to thank everyone for their kind wishes and prayers," said the statement from Nina Pham.

"I am blessed by the support of family and friends and am blessed to be cared for by the best team of doctors and nurses in the world here at Texas Health Presbyterian Hospital Dallas."

Pham, 26, was infected with the hemorrhagic virus while caring for Thomas Eric Duncan, who arrived in Texas in late September, soon began to show symptoms of Ebola and eventually died last week.

He is believed to have been infected in Liberia.

The Centres for Disease Control and Prevention has said Pham's infection must have resulted from a breach of protocol, though no specific fault has yet been found in the way Pham put on or took off her protective gear.

Pham's infection - the first case of Ebola transmission on US soil - was announced early Sunday.

The world's largest outbreak of Ebola in West Africa has claimed more than 4,000 lives since the beginning of the year, particularly in Sierra Leone, Liberia and Guinea.

A handful of Americans who have been infected while working in Africa have been airlifted back to the United States for treatment and survived, including three medical missionaries and a freelance photojournalist.

"We are working tirelessly to help her in this courageous fight," said the hospital's chief executive officer Barclay Berdan.

"The doctors and nurses involved with her treatment remain hopeful, and we ask for the prayers of the entire country."