A second healthcare worker in the US state of Texas has tested positive for Ebola, health officials have said.
Both health workers treated Liberian man Thomas Eric Duncan, who died last week after becoming the first person diagnosed with Ebola in the US.
A senior Dallas official said there was a "real possibility" of further cases, and contingencies were being prepared.
Meanwhile, the UN's Ebola mission chief says the world is falling behind in the race to contain the virus.
The World Health Organization (WHO) says 4,447 people have died from the outbreak, mainly in West Africa.
Sierra Leone, Liberia and Guinea have been hardest hit by the outbreak, which began in December 2013 but was confirmed in March.
President Barack Obama is due to hold a video conference with British, French, German and Italian leaders to discuss the Ebola crisis later on Wednesday.
The identity of the second Texas health worker has not yet been revealed.
But Texas health officials said she was a woman who lived alone without pets.
The disposition of the pets of people infected with Ebola has been a concern - the first woman infected in the US with Ebola had a dog, as did a nurse infected in a Spanish hospital.
In Dallas, the second infected healthcare worker was placed in isolation within 90 minutes of reporting a fever.
Daniel Varga, the chief clinical officer of hospital operator Texas Health Resources, told a joint news conference that she was involved in the care of Mr Duncan and was exposed to the virus some time during his treatment.
But Dallas County Judge Clay Jenkins said the authorities were preparing for more possible cases.
"We are preparing contingencies for more, and that is a very real possibility," he said.
Dallas Mayor Mike Rawlings said it might take time to deal with the outbreak, but the authorities were "not fearful".
"We can only beat this moment by moment, person by person, detail by detail," he said at the news conference.
"It may get worse before it gets better, but it will get better."
Last weekend, officials said nurse Nina Pham, 26, had been exposed to Ebola at Texas Health Presbyterian Hospital, where she was involved in Mr Duncan's care.
Doctors at the hospital said she was "doing well" on Tuesday.
By James Gallagher, BBC health editor
This is a reminder that Ebola is a dangerous threat even within some of the best hospitals in world.
This is the second case of transmission in Texas, on top of the case in Spain.
Protective gear should minimise the risk to health workers treating Ebola patients.
But worryingly there have been reports of staff not getting the correct equipment or the necessary training.
These isolated cases should not become an outbreak as authorities in both countries are monitoring those who came into contact with infected people.
But each new case of transmission is asking the question - is enough being done to protect healthcare workers?
A total of 75 healthcare workers were being monitored for symptoms following the second diagnosed case linked to Duncan.
Mr Varga refused to comment on allegations from nurses at the Dallas hospital that health workers had been without adequate protective clothing for days during the outbreak.
The nurses also said they had received little guidance on how to prevent the spread of the virus, that Duncan was not immediately isolated from other patients when he was admitted to the hospital a second time, and that medical waste was allowed to pile up at least once.
Ebola patients treated outside West Africa*
*In all but three cases the patient was infected with Ebola while in West Africa. Infection outside Africa has been restricted to health workers in Madrid and in Dallas. DR Congo has also reported a separate outbreak of an unrelated strain of Ebola.
- Avoid direct contact with sick patients as the virus is spread through contaminated body fluids
- Wear goggles to protect eyes
- Clothing and clinical waste should be incinerated and any medical equipment that needs to be kept should be decontaminated
- People who recover from Ebola should abstain from sex or use condoms for three months
It comes after CDC chief Thomas Frieden said there had been a breach of protocol by health workers that led to Ms Pham's infection.
"The CDC is saying that protocols were breached, but the nurses are saying there were no protocols," the head of the national nurses union, Roseann DeMoro, told reporters on Tuesday.
There have been 8,914 Ebola cases overall, including the fatal cases, and the WHO says it expects this number to top 9,000 by the end of the week.
Anthony Banbury told a special session of the UN Security Council on Tuesday that if Ebola was not stopped now, the world would "face an entirely unprecedented situation for which we do not have a plan".
In other developments:
- Liberia's transport minister has gone into quarantine after her driver died from Ebola
- A football player for Sierra Leone's national team says his team-mates have been stigmatised and humiliated by the outbreak
- The World Health Organization (WHO) warns the infection rate could reach 5,000 to 10,000 new cases a week in two months if efforts are not stepped up
- The WHO says it will declare the end of the outbreak in Senegal at the end of this week (17 October) and in Nigeria next week (20 October), if no new cases are detected before then
The WHO estimates its figures by taking the numbers of confirmed cases and multiplying them - from Guinea by 1.5, from Sierra Leone by 2 and from Liberia by 2.5 - to account for under-reporting.
Protective Ebola suit×
The cap forms part of a protective hood covering the head and neck. It offers medical workers an added layer of protection, ensuring that they cannot touch any part of their face whilst in the treatment centre.
Goggles, or eye visors, are used to provide cover to the eyes, protecting them from splashes. The goggles are sprayed with an anti-fogging solution before being worn. On October 21, the US Centers for Disease Control and Prevention (CDC) announced stringent new guidelines for healthcare personnel who may be dealing with Ebola patients. In the new guidelines, health workers are advised to use a single use disposable full face shield as goggles may not provide complete skin coverage.
Covers the mouth to protect from sprays of blood or body fluids from patients. When wearing a respirator, the medical worker must tear this outer mask to allow the respirator through.
A respirator is worn to protect the wearer from a patient's coughs. According to guidelines from the medical charity Medecins Sans Frontieres (MSF), the respirator should be put on second, right after donning the overalls.
A surgical scrub suit, durable hospital clothing that absorbs liquid and is easily cleaned, is worn as a baselayer underneath the overalls. It is normally tucked into rubber boots to ensure no skin is exposed.
The overalls are placed on top of the scrubs. These suits are similar to hazardous material (hazmat) suits worn in toxic environments. The team member supervising the process should check that the equipment is not damaged.
A minimum two sets of gloves are required, covering the suit cuff. When putting on the gloves, care must be taken to ensure that no skin is exposed and that they are worn in such a way that any fluid on the sleeve will run off the suit and glove. Medical workers must change gloves between patients, performing thorough hand hygiene before donning a new pair. Heavy duty gloves are used whenever workers need to handle infectious waste.
A waterproof apron is placed on top of the overalls as a final layer of protective clothing.
Ebola health workers typically wear rubber boots, with the scrubs tucked into the footwear. If boots are unavailable, workers must wear closed, puncture and fluid-resistant shoes.