The head of the Centers for Disease Control and Prevention warned Monday that other U.S. hospital workers may have Ebola after a Dallas nurse tested positive for the virus, as he vowed to "double down" on training for health care workers -- raising questions about whether he told the truth when he initially assured the public and Congress that U.S. hospitals are capable of treating Ebola patients.

Thomas Frieden, at a press briefing on Monday, said the CDC would be taking a number of steps including offering more training and outreach throughout the health care system. He said they need to "rethink" their approach to the virus.

"I feel awful that a health care worker became infected in the care of an Ebola patient," Frieden said.

But he urged the public to brace for more bad news.

"We need to consider the possibility that there could be additional cases, particularly among the health care workers who cared for" Ebola patient Thomas Eric Duncan, he said, adding: "We're concerned that there could be other infections in the coming days."

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Frieden also voiced regret for initially describing the latest infection as a "protocol breach," which some interpreted as blaming the nurse. "I'm sorry if that was the impression given. That was certainly not my intention," he said.

Frieden vowed to implement an "immediate set of steps" to ensure that those caring for the infected nurse are safe.

But just two weeks ago, Frieden claimed that "virtually any hospital in the country that can do isolation can do isolation for Ebola."

The CDC director repeatedly has said U.S. hospitals know how to stop the spread of Ebola, even though it is difficult. He said in written testimony to a House foreign affairs subcommittee in August that: "We know how to stop Ebola with strict infection control practices which are already in widespread use in American hospitals, and by stopping it at the source in Africa."

Reflecting the urgency of the developments in Texas, President Obama met Monday afternoon with senior administration officials on the Ebola response in the Oval Office. Frieden has launched an investigation as to how the Dallas nurse became infected.

However, some have complained the case shows how many hospitals are inadequately trained to handle the virus, which has killed more than 4,000 people during the latest outbreak in West Africa.

"You don't scapegoat and blame when you have a disease outbreak," Bonnie Castillo of National Nurses United told Reuters on Sunday. "We have a system failure. That is what we have to correct."

"We haven't provided [caregivers] with a national training program. We haven't provided them with the necessary experts that have actually worked in hospitals with Ebola," said Dr. Gavin McGregor-Skinner of Penn State University, an expert in public health preparedness.

Separately, some have raised concerns that no single person or agency is in charge of the U.S. response.

Texas and CDC officials say that the nurse in question was wearing the recommended personal protective gear for handling an Ebola patient, including a gown, gloves, mask, and eye shield. However, one expert told Reuters that gear only offers a minimum amount of protection, especially when the disease enters its final phases.

On Sunday, hazmat crews cleaned and disinfected the woman's apartment. KDFW reported that members of the 15-person crew took items out of the apartment and placed them in metal drums to be taken away.

The Morning News also reported that the woman owns a King Charles Spaniel dog. There was no sign that the dog had contracted the virus, but Dallas Mayor Mike Rawlings said Sunday morning that officials had a "plan to take care of the pet." Dallas police reported that a worker in protective gear had entered the nurse's apartment Sunday evening to give the dog food and water.

Last week, a dog belonging to an Ebola-infected nurse was euthanized in Spain, causing a national outcry.

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