WASHINGTON—The White House on Wednesday acknowledged shortcomings in the government’s response to Ebola as lawmakers from both parties called for swifter action to contain the spread of the virus.

President Barack Obama tried to contain the fallout from the diagnosis of a second Texas health worker with Ebola, saying he ordered the Centers for Disease Control and Prevention to send a rapid response team to oversee the handling of any future infections in the U.S. within 24 hours of diagnosis.

Mr. Obama, speaking after meeting for more than 90 minutes with his senior advisers involved in the Ebola response, promised a review of every step of the government’s response since the first case appeared in the U.S. He said U.S. officials will more aggressively monitor incidents where the virus could potentially spread and apply “lessons learned” from apparent breakdowns in the government’s response to any future cases.

At the same time, he tried to tamp down public fear of the virus by saying the dangers of an outbreak in the U.S. continue to be low. He pointed to his visit last month with health care officials at Emory University who had treated a patient who had contracted Ebola while in West Africa.

“I shook hands with, hugged and kissed not the doctors but a couple of the nurses at Emory,” he said. “They followed the protocols. They knew what they were doing, and I felt perfectly safe doing so.”