Authorities have confirmed that 18 people have been quarantined, in Madrid and the Canary Islands.
Elsewhere, a nurse who is being treated for Ebola in Texas was moved to an isolation unit in Maryland for further treatment on Thursday.
She had been tending to a Liberian man, who died from the virus.
US President Barack Obama is resisting calls for a travel ban from West African countries to stem the spread of the disease.
“If we institute a travel ban instead of the protocols we have put in place now, history shows there is a likelihood of increased avoidance. They may engage in something called ‘broken travel’. Essentially breaking up their trip so they can hide the fact they have been to one of these countries where there is a disease in place”.
Washington has ordered 4,000 reservists to West Africa to help in the fight. Obama says he may even appoint an Ebola Czar to advise him.
A team of British army medics is already in the region, setting up a new treatment centre. A Royal Navy ship, with a fully equipped hospital will reach African waters by the end of the month.
Ebola has so far killed 4,500 people, mostly in Guinea, Liberia, and Siera Leone.
Officials in West Africa are preparing for the worst, ordering additional stocks of essential supplies, from protective suits and masks, to body bags.