WASHINGTON — President Trump is pressing his health officials to pursue a crash development program for a coronavirus vaccine that could be widely distributed by the beginning of next year, despite widespread skepticism that such an effort could succeed and considerable concern about the implications for safety.

The White House has made no public announcement of the new effort, called Operation Warp Speed, and some officials are apparently trying to talk the president down, telling him that it would be more harmful to set an unreasonably short deadline that might result in a faulty vaccine than to wait for one that is proved safe and effective.

But after the existence of the effort was first reported on Wednesday by Bloomberg News, the Department of Health and Human Services confirmed it. “Operation Warp Speed is clearly another extension of President Trump’s bold leadership and unwillingness to accept ‘business as usual’ approaches to addressing the Covid-19 crisis,” said Michael Caputo, the department’s assistant secretary for public affairs.

Mr. Trump’s order came after he grew frustrated by warnings from Dr. Anthony S. Fauci, the director of the National Institute of Allergy and Infectious Diseases, and other experts on the coronavirus task force, that development of a vaccine would take a year to 18 months, and that even that schedule might be ambitious. He told Alex M. Azar II, the health and human services secretary, to come up with a faster program.

According to one official, the idea would be to indemnify the major pharmaceutical and biotechnology companies from liability if the vaccines cause sickness or death, and to involve the Pentagon in the testing program. But most of the military’s efforts have focused on defenses against biological weapons, not viruses that arise naturally or are transmitted by community spread.

Seventy to 100 companies, groups and academic institutions around the world are working on vaccines, including Oxford University and several projects in China. But many of the most experienced vaccine makers and experts are in the United States.

Mr. Trump’s policymakers and image handlers may be trying to consolidate, under one name, a series of efforts already underway. Almost as soon as the coronavirus outbreak began, the Biomedical Advanced Research and Development Authority, part of the Department of Health and Human Services, issued grants totaling about $1 billion to two big U.S.-based companies, Johnson & Johnson and Moderna, to speed development of different approaches to a vaccine.

Most of that money is for research and clinical trials; Moderna is headed into Phase 2 trials. Last week Johnson & Johnson, which hopes to begin trials of its most promising potential vaccine at latest by the first week of September, announced that it had struck a deal with a firm called Emergent BioSolutions in Maryland, to mass produce its product — even though it is far from approval. Emergent BioSolutions was essentially created by the government years ago to provide a manufacturing base for vaccines in case of an emergency.

It is not clear how much more money the administration is willing to put behind the operation, or how advanced the project is. Mr. Azar was asked to begin the effort, but he has been sidelined from many elements of the administration’s response amid clashes with other officials and is believed to be on thin ice with Mr. Trump.

Mr. Trump, in the middle of a re-election campaign, may be satisfied with declarations that a vaccine is coming soon. And even before any vaccine receives formal approval, it could be designated for “emergency use,” meaning that it could be given to health professionals.

When companies say that it will take at least a year to 18 months to develop a vaccine, they are sometimes counting from January — when China provided the genetic code of the virus — and sometimes from when the firms began to work toward a solution.

But the timing is not completely within their control. Much depends on the success of the trials and review by the Food and Drug Administration. Most other countries have a similar process.

In more normal times, a vaccine can take upward of a decade to get through all the regulatory approvals. Some officials note the dangers of rushing: During the Ford administration, a rushed vaccine for swine flu caused several dozen deaths and damaging side effects.

But Mr. Trump has made no secret of his impatience with the warnings, from Dr. Fauci and others, about how long it takes to prove both the safety and the efficacy of a vaccine through clinical trials. In a meeting with pharmaceutical and biotechnology executives on March 2, before deaths from the virus started mounting in large numbers, Mr. Trump interrupted several times to ask how long it would take for each of the executives to get into production.

“So you’re talking over the next few months, you think you could have a vaccine,” Mr. Trump said to one executive. He answered: “Correct. Correct. With Phase 2.”

Dr. Fauci intervened: “Yeah, you won’t have a vaccine. You’ll have a vaccine to go into testing.” Then he added, “A year to a year and a half.”

Mr. Trump responded: “A couple of months, right? I mean, I like the sound of a couple of months better, I must be honest with you.”

Sheryl Gay Stolberg contributed reporting.