Spanish health authorities said on Sunday there were signs of hope for a nurse infected with Ebola in Madrid as the levels of the virus in her body were diminishing, though they also said she remained in a serious condition.

Teresa Romero, 44, became the first known person to become infected with Ebola outside Africa during the current outbreak after she cared for two infected priests repatriated to Spain for treatment. The priests later died.

"The patient appears to be in a stable condition ... There are some signs that could give us cause for some hope," Fernando Simon, a high level official at Spain's Health Ministry, told a news conference.

"There are high hopes that the infection is starting to come under control," he said, adding she was not yet out of danger.

"We have to be very cautious," Simon said.

The worst ever Ebola outbreak has killed over 4,000 people, mostly in West Africa, although the disease - which causes hemorrhagic fever and is passed on through direct contact with body fluids from an infected person - has started spreading elsewhere.

A health worker in Texas tested positive for the disease in a preliminary test, the state's health department said on Sunday. The worker had helped care for Thomas Eric Duncan, who was diagnosed with Ebola in the United States after arriving from his native Liberia. He died last week.

Romero has spent the past week in hospital and had taken a turn for the worse a few days ago. On Saturday evening, however, she was conscious and was responding to hospital staff after being given antibodies from previously infected patients.

Spain is still investigating how exactly Romero could have contracted the disease, amid recriminations over the government's handling of the case.

Some Spanish media have said Romero has been treated with ZMab, a combination drug made by Canada-based company Defyrus Inc. ZMab is one of the agents used to make ZMapp, an experimental treatment which has been used on some Ebola sufferers, a number of whom survived.

Spanish authorities have not confirmed the reports. A health source said ZMab was available in Spain but could not confirm whether it had been used in Romero's case.

Fifteen people, including Romero's husband, are being monitored for signs of Ebola in a special isolation unit of Madrid's Carlos III hospital. None have so far shown any symptoms.