WASHINGTON — Beneath the calming reassurance that President Obama has repeatedly offered during the Ebola crisis, there is a deepening frustration, even anger, with how the government has handled key elements of the response.

Those frustrations spilled over when Mr. Obama convened his top aides in the Cabinet room after canceling his schedule on Wednesday. Medical officials were providing information that later turned out to be wrong. Guidance to local health teams was not adequate. It was unclear which Ebola patients belonged in which threat categories.

“It’s not tight,” a visibly angry Mr. Obama said of the response, according to people briefed on the meeting. He told aides they needed to get ahead of events and demanded a more hands-on approach, particularly from the Centers for Disease Control and Prevention. “He was not satisfied with the response,” a senior official said.

The difference between the public and private messages illustrates the dilemma Mr. Obama faces on Ebola — and a range of other national security issues — as he tries to galvanize the response to a public health scare while not adding to the sense of panic fueled by 24-hour cable TV and the nonstop Twitter chatter.