Investigations are under way at a hospital in Madrid after a Spanish nurse became the first person known to have contracted the deadly Ebola virus outside West Africa.
The nurse had treated two Spanish missionaries who died of the disease after being flown home from the region.
Meanwhile, US President Barack Obama has announced plans to screen passengers flying to the United States.
Some 3,400 people have died in the outbreak - mostly in West Africa.
The Spanish auxiliary nurse, a 40-year-old woman who has not been named, was one of about 30 staff at the Carlos III hospital in Madrid who had been treating priests Manuel Garcia Viejo and Miguel Pajares, officials say.
Mr Garcia Viejo, 69, died at the hospital on 25 September after catching Ebola in Sierra Leone. Miguel Pajares, 75, died in August after contracting the virus in Liberia.
The nurse was moved to Carlos III hospital in Madrid in the early hours of Tuesday
The nurse had twice gone into the room where Mr Garcia Viejo had been treated - to be directly involved in his care and to disinfect the room after his death. Both times she was wearing protective clothing.
Madrid health care director Antonia Alemany told reporters that according to the information available: "The nurse went into the room wearing the individual protection gear and there's no knowledge of an accidental exposure to risk."
Shortly afterwards the nurse went on holiday, a hospital spokesman said, but fell ill on 30 September and was admitted to Alcorcon hospital in south-west Madrid on Sunday after being tested positive for Ebola.
Early on Tuesday she was moved under police escort to Carlos III hospital in the capital and is said to be in a stable condition.
Her husband and the other members of the medical team are being monitored. It was not known where she had gone on holiday.
In Sierra Leone, Ebola treatment centres are full and patients are being turned away, as Tulip Mazumdar reports
It is also unclear how she could have contracted Ebola.
The hospital was reported to have had extreme protective measures in place including two sets of overalls, gloves and goggles.
However, health workers told El Pais newspaper that the clothing used during the treatment of the two priests did not have level-four biological security, which is fully waterproof and with independent breathing apparatus.
Instead it was level two, the paper says, as photographs provided by staff indicated that the overalls worn did not allow for ventilation and the gloves were made of latex and bound with adhesive tape.
Manuel Garcia Viejo, seen in a file photo, was the second Spanish priest to be repatriated from Africa with Ebola
Containing Ebola: BBC health correspondent Michelle Roberts
Patients should be isolated - ideally in a hospital with the highest level of bio-safety.
Such a facility would use a specially-designed tent with controlled ventilation to house the patient's bed - this allows staff to provide clinical care while containing the infection.
Staff treating the patient must wear protective suits, gloves, masks and goggles. This equipment should be completely impermeable since Ebola is spread in bodily fluids such as sweat, urine and blood
Any clinical waste such as syringes, paper towels or clothing from the patient should incinerated. A dedicated laboratory should be used to carry out any necessary tests.
Marc Sprenger, director of the European Centre for Disease Control and Prevention, told the BBC that Spanish officials had to trace any contacts the nurse may have made after she started showing symptoms.
"It's extremely important. We need to follow up all contacts in Europe and I'm sure that the Spanish authorities are doing this. It's a very serious business," he said.
In the US, President Obama said on Monday that the likelihood of an Ebola outbreak there was "extremely low", but "we don't have a lot of margin of error".
He criticised foreign governments for not acting "as aggressively as they need to" against the outbreak.
Ebola spreads through contact with bodily fluids and the only way to stop an outbreak is to isolate those who are infected.
In another development, Sierra Leone opposition politician Chernor Bah says a shipment of supplies urgently needed to help Ebola patients has been held up for months in Freetown port because the government refuses to pay duty on it.
However, health officials insist payment to allow the shipment through has been made.
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.
Thomas Duncan, the first person to be diagnosed with Ebola in the US, is being treated at a Dallas hospital. He caught the virus in his native Liberia. Doctors say he is critical but stable.
Ebola virus disease (EVD)
Symptoms include high fever, bleeding and central nervous system damage
Spread by body fluids, such as blood and saliva
Fatality rate can reach 90% - but current outbreak has mortality rate of about 70%
The nurse had treated two Spanish missionaries who died of the disease after being flown home from the region.
Meanwhile, US President Barack Obama has announced plans to screen passengers flying to the United States.
Some 3,400 people have died in the outbreak - mostly in West Africa.
The Spanish auxiliary nurse, a 40-year-old woman who has not been named, was one of about 30 staff at the Carlos III hospital in Madrid who had been treating priests Manuel Garcia Viejo and Miguel Pajares, officials say.
Mr Garcia Viejo, 69, died at the hospital on 25 September after catching Ebola in Sierra Leone. Miguel Pajares, 75, died in August after contracting the virus in Liberia.
The nurse was moved to Carlos III hospital in Madrid in the early hours of Tuesday
The nurse had twice gone into the room where Mr Garcia Viejo had been treated - to be directly involved in his care and to disinfect the room after his death. Both times she was wearing protective clothing.
Madrid health care director Antonia Alemany told reporters that according to the information available: "The nurse went into the room wearing the individual protection gear and there's no knowledge of an accidental exposure to risk."
Shortly afterwards the nurse went on holiday, a hospital spokesman said, but fell ill on 30 September and was admitted to Alcorcon hospital in south-west Madrid on Sunday after being tested positive for Ebola.
Early on Tuesday she was moved under police escort to Carlos III hospital in the capital and is said to be in a stable condition.
Her husband and the other members of the medical team are being monitored. It was not known where she had gone on holiday.
In Sierra Leone, Ebola treatment centres are full and patients are being turned away, as Tulip Mazumdar reports
It is also unclear how she could have contracted Ebola.
The hospital was reported to have had extreme protective measures in place including two sets of overalls, gloves and goggles.
However, health workers told El Pais newspaper that the clothing used during the treatment of the two priests did not have level-four biological security, which is fully waterproof and with independent breathing apparatus.
Instead it was level two, the paper says, as photographs provided by staff indicated that the overalls worn did not allow for ventilation and the gloves were made of latex and bound with adhesive tape.
Manuel Garcia Viejo, seen in a file photo, was the second Spanish priest to be repatriated from Africa with Ebola
Containing Ebola: BBC health correspondent Michelle Roberts
Patients should be isolated - ideally in a hospital with the highest level of bio-safety.
Such a facility would use a specially-designed tent with controlled ventilation to house the patient's bed - this allows staff to provide clinical care while containing the infection.
Staff treating the patient must wear protective suits, gloves, masks and goggles. This equipment should be completely impermeable since Ebola is spread in bodily fluids such as sweat, urine and blood
Any clinical waste such as syringes, paper towels or clothing from the patient should incinerated. A dedicated laboratory should be used to carry out any necessary tests.
Marc Sprenger, director of the European Centre for Disease Control and Prevention, told the BBC that Spanish officials had to trace any contacts the nurse may have made after she started showing symptoms.
"It's extremely important. We need to follow up all contacts in Europe and I'm sure that the Spanish authorities are doing this. It's a very serious business," he said.
In the US, President Obama said on Monday that the likelihood of an Ebola outbreak there was "extremely low", but "we don't have a lot of margin of error".
He criticised foreign governments for not acting "as aggressively as they need to" against the outbreak.
Ebola spreads through contact with bodily fluids and the only way to stop an outbreak is to isolate those who are infected.
In another development, Sierra Leone opposition politician Chernor Bah says a shipment of supplies urgently needed to help Ebola patients has been held up for months in Freetown port because the government refuses to pay duty on it.
However, health officials insist payment to allow the shipment through has been made.
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.
Thomas Duncan, the first person to be diagnosed with Ebola in the US, is being treated at a Dallas hospital. He caught the virus in his native Liberia. Doctors say he is critical but stable.
Ebola virus disease (EVD)
Symptoms include high fever, bleeding and central nervous system damage
Spread by body fluids, such as blood and saliva
Fatality rate can reach 90% - but current outbreak has mortality rate of about 70%
Incubation period is two to 21 days
There is no proven vaccine or cure
Supportive care such as rehydrating patients who have diarrhoea and vomiting can help recovery
Fruit bats, a delicacy for some West Africans, are considered to be virus's natural host
Are you affected by the issues raised in this story? You can email your experiences to haveyoursay@bbc.co.uk