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.