Doctors treating a Spanish nurse infected with the deadly Ebola virus were cautiously optimistic about her condition on Tuesday after she survived the potentially critical two-week period after being infected.

"She is in stable condition, and this is a good day, the 15th day" since she first showed symptoms of the illness, said Marta Arsuaga, a doctor at the specialist tropical disease hospital Carlos III.

"Statistics show that usually the disease is most deadly up to the 13th or 14th day. Now it is one day after that, so that is good," she told reporters at the hospital.

The infected nurse - 44-year-old Teresa Romero - is thought to have caught Ebola in Carlos III while treating an elderly missionary who was infected in Sierra Leone and died on Sept 25.

Romero is the first person known to have caught Ebola outside Africa, where the current outbreak has killed more than 4,000 people, according to the World Health Organization.

She first noticed her own symptoms on Sept 29 and was hospitalized on Oct 6.

Doctors said she was in "serious but stable" condition.

"We trust this condition will be maintained," Arsuaga said, although she cautioned that the critical phase can vary and be subject to "complications".

The doctor said she was unable to forecast a date that Romero was likely to be declared out of danger.

Meanwhile, a United Nations medical worker who was infected with Ebola in Liberia has died despite "intensive medical procedures", a German hospital said on Tuesday.

The St. Georg hospital in Leipzig said the 56-year-old man, whose name has not been released, died overnight of the infection.

The man tested positive for Ebola on Oct 6.

AFP - Reuters