Updated 7:15 p.m.

President Barack Obama vowed Wednesday that his administration would respond in a "much more aggressive way" to cases of Ebola in the United States and warned that in an age of frequent travel the disease could spread globally if the world doesn't respond to the "raging epidemic in West Africa."

In his most urgent comments on the spread of the disease, Obama also sought to ease growing anxiety and fears in the U.S. in the aftermath of a second nurse being diagnosed with Ebola after treating a patient in a Dallas hospital. He said he had directed the Centers for Disease Control and Prevention to step up its response to new cases.

"We want a rapid response team, a SWAT team essentially, from the CDC to be on the ground as quickly as possible, hopefully within 24 hours, so that they are taking the local hospital step by step though what needs to be done," he said.

Obama spoke after cancelling a political campaign trip to convene a session of top Cabinet officials involved in the Ebola response both in the U.S. and in the West African region where the disease has been spreading at alarming rates.

Participants in the meeting were a roster of Cabinet secretaries and top Obama advisers, including Defense Secretary Chuck Hagel, Attorney General Eric Holder, Health and Human Services Secretary Sylvia Burwell and Joint Chiefs of Staff Chairman Gen. Martin Dempsey.

Even as he raised the potential for global contagion, Obama also stressed that the danger in the United States remained a long shot.

"Here's what we know about Ebola. It's not like the flu. It's not airborne," he said.

He made the point of noting that when he visited with health care workers who had attended to Ebola patients at Emory University Hospital in Atlanta, he hugged and kissed them without fear of infection. "They followed the protocols, they knew what they were doing," he said. "I felt perfectly safe doing so."

Second Texas nurse tests positive

Medical records provided to The Associated Press by Thomas Eric Duncan's family show 29-year-old nurse Amber Joy Vinson inserted catheters, drew blood, and dealt with Duncan's body fluids before he died last week. It's not clear how she contracted the virus.

Kent State University in Ohio says three employees are related to a Vinson, who visited family in Ohio and flew from Cleveland to Dallas shortly before she was diagnosed Wednesday.

A Frontier Airlines employee wears rubber gloves as she directs passengers where to go at Cleveland Hopkins International Airport Wednesday, Oct. 15, 2014, in Cleveland. Tony Dejak / AP

A university statement says the woman is a graduate of Kent State, receiving degrees in 2006 and 2008, but didn't visit the college's campus on her most recent visit.

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Infected Ebola patients are not considered contagious until they have symptoms. The airplane crew said the woman had no symptoms during Frontier Airlines Flight 1143 from Cleveland to Dallas-Fort Worth on Monday. She flew from Dallas to Cleveland on Oct. 10.

The CDC said it is alerting the 132 passengers who were on the return flight "because of the proximity in time between the evening flight and first report of illness the following morning." Officials are asking them to call the health agency so they can be monitored.

The federal Centers for Disease Control and Prevention said the additional infection is "a serious concern."

"What happened there (in Dallas), regardless of the reason, is not acceptable. It shouldn't have happened," Anthony Fauci, director of the Institute of Allergy and Infectious Diseases of NIH, said Wednesday on MSNBC.

CDC sees need to step up response

The nurse was monitoring herself for symptoms, Dallas County Judge Clay Jenkins said. She reported a fever Tuesday and was in isolation within 90 minutes, Jenkins said.

Hazmat workers with Protect Environmental unload barrels in preparation for decontaminating an apartment at The Village Bend East apartment complex where a second health care worker who has tested positive for the Ebola virus resides on October 15, 2014 in Dallas, Texas. Mike Stone / Getty Images

"We are looking at every element of our personal protection equipment and infection control in the hospital," said Dr. Daniel Varga, chief clinical officer for Texas Health Resources, which operates Texas Health Presbyterian Hospital Dallas.

Dr. Tom Frieden, head of the CDC, has acknowledged that the government was not aggressive enough in managing Ebola and containing the virus as it spread from an infected patient to a nurse at a Dallas hospital.

"We could've sent a more robust hospital infection control team and been more hands-on with the hospital from day one about exactly how this should be managed," he said Tuesday.

The second case may help health officials determine where the infection-control breach is occurring and make practices safer for health workers everywhere. For example, if both health workers were involved in drawing Duncan's blood, placing an intravenous line or suctioning mucus when Duncan was on a breathing machine, that would be recognized as a particularly high-risk activity. It might also reveal which body fluids pose the greatest risk.

Emergency responders in hazardous-materials suits began decontamination work before dawn Wednesday at the Dallas apartment complex where the second nurse lives. Officials said she lives alone with no pets.

Notices handed out to neighbors advise that "a health care worker who lives in your area has tested positive for Ebola."

Ryan Fus, 24, who lives in the same building as the blocked-off apartment, said police knocked on his door before 6 a.m. to notify him and make sure he was all right.

"It's a little scary. It's a little shocking that it's right near me," he said.

Health care workers concerned

Dallas city spokeswoman Sana Syed said a hazardous-materials crew has finished cleaning common areas of the complex and that the state was sending a crew to clean the actual apartment.

Frieden outlined new steps this week designed to stop the spread of the disease, including the creation of an Ebola response team, increased training for health care workers nationwide and changes at the Texas hospital to minimize the risk of more infections.

The new case lends support to nurses' claims this week that they have inadequate training and in some cases, protective gear, to take care of Ebola patients.

"They're not prepared" for what they are being asked to do, said RoseAnn DeMoro, executive director of National Nurses United, a union with 185,000 members.

Based on statements from nurses it did not identify, the union described how Duncan was left in an open area of the emergency room for hours. It said staff treated Duncan for days without the correct protective gear, that hazardous waste was allowed to pile up to the ceiling and safety protocols constantly changed.

DeMoro refused to say how many nurses made the statement about Texas Health Presbyterian Hospital, but insisted they were in a position to know what happened.

Officials say at least 76 people at the hospital might have been exposed, and all are being monitored for fever and other symptoms.

Nurse Nina Pham, 26, contracted the virus while caring for Duncan. Health officials are monitoring 48 others who had some contact with Duncan before he was admitted to the hospital where he died.

Pham became the first person to contract the disease on U.S. soil. She released a statement Tuesday through the hospital saying she was "doing well." The hospital listed her in good condition. She has received a plasma transfusion from a doctor who recovered from the virus.