The WHO adviser, Prof. Peter Piot, said he was not surprised that a Spanish nurse had contracted the disease.
The nurse, Teresa Romero, is the first person known to have contracted the deadly virus outside West Africa.
She treated two Spanish missionaries who died of Ebola in Madrid.
Teresa Romero, a 40-year-old auxiliary nurse, had been part of a team of about 30 staff at the Carlos III hospital in Madrid looking after Manuel Garcia Viejo and Miguel Pajares when they were repatriated from Sierra Leone and Liberia respectively.
She remains in quarantine in the Spanish capital along with her husband and three other people.
A fifth person was admitted on Wednesday morning with a slight fever. She is said to be a friend of Teresa Romero and, like her, an auxiliary nurse in the Carlos III Ebola care unit.
In all, more than 50 people in Spain are under observation.
Teresa Romero told El Mundo on October 8 that she had followed the correct protocol and had “no idea” how she had become infected. She said she was feeling “a little better” but was very tired.
Officials say earlier she had twice gone into Manuel Garcia Viejo’s hospital room, first to treat him and later to disinfect the room after his death.
Spanish media say neighbors of the infected nurse have been calling emergency services, asking how to protect their children after sharing lifts and public spaces.
Promising “total transparency”, Spanish PM Mariano Rajoy appealed for calm while at the same time urging vigilance.
“Let the professionals do their work. Spain’s health system is one of the best in the world,” he told parliament on October 8.
In another development, Teresa Romero’s husband, Javier Limon, is reported to be fighting a court order to have their pet dog put down over fears that it could be carrying the disease. Animal rights groups have also criticized the move, saying there is no evidence that Ebola has been spread by dogs.
Some 3,400 people have died in the current Ebola outbreak with most of the deaths in Guinea, Sierra Leone and Liberia.
There have been nearly 7,500 confirmed Ebola infections worldwide, with officials saying the figure is likely to be much higher in reality.
WHO experts have insisted that modern hospitals with rigorous disease control measures would prevent infection – but the case of the Madrid nurse proves that is far more difficult than many thought.
Prof. Peter Piot, a world specialist in Ebola brought in by the WHO as a scientific adviser, warned that even the simplest movement, like rubbing your eyes, is a risk.
“The smallest mistake can be fatal,” he said.
“For example, a very dangerous moment is when you come out of the isolation unit you take off your protective gear, you are full of sweat and so on.”
Many of those who have died of Ebola in West Africa have been health care workers.
Meanwhile the US military is stepping up its efforts to respond to the Ebola outbreak in Liberia, Sierra Leone and Guinea.
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