WASHINGTON — The shortage of vaccines to combat a fast-growing monkeypox outbreak was caused in part because the Department of Health and Human Services failed early on to ask that bulk stocks of the vaccine it already owned be bottled for distribution, according to multiple administration officials familiar with the matter.

By the time the federal government placed its orders, the vaccine’s Denmark-based manufacturer, Bavarian Nordic, had booked other clients and was unable to do the work for months, officials said — even though the federal government had invested well over $1 billion in the vaccine’s development.

The government is now distributing about 1.1 million doses, less than a third of the 3.5 million that health officials now estimate are needed to fight the outbreak. It does not expect the next delivery, of half a million doses, until October. Most of the other 5.5 million doses the United States has ordered are not scheduled to be delivered until next year, according to the federal health agency.

To speed up deliveries, the government is scrambling to find another firm to take over some of the bottling, capping and labeling of frozen bulk vaccine that is being stored in large plastic bags at Bavarian Nordic’s headquarters outside Copenhagen. Because that final manufacturing phase, known as fill and finish, is highly specialized, experts estimate it will take another company at least three months to gear up. Negotiations are ongoing with Grand River Aseptic Manufacturing, a Michigan factory that has helped produce Covid-19 vaccines, to bottle 2.5 million of the doses now on order, hopefully shaving months off the timetable, according to people familiar with the situation.

Health and Human Services officials so miscalculated the need that on May 23, they allowed Bavarian Nordic to deliver about 215,000 fully finished doses that the federal government had already bought to European countries instead of holding them for the United States.

At the time, the nation had only eight confirmed monkeypox cases, agency officials said. And it could not have used those doses immediately because the Food and Drug Administration had not yet certified the plant where the vaccine, Jynneos, was poured into vials.

But it could now. Some states are trying to stretch out doses by giving recipients only one shot of the two-dose vaccine. California, Illinois and New York have declared public health emergencies. In New York City, every available slot for a monkeypox shot is taken.

Lawrence O. Gostin, a former adviser to the Centers for Disease Control and Prevention who has consulted with the White House about monkeypox, said the government’s response has been hobbled by “the same kinds of bureaucratic delays and forgetfulness and dropping the ball that we did during the Covid pandemic.”

The obstacles to filling and finishing vials follow other missteps that have limited vaccine supply. The United States once had some 20 million doses in a national stockpile but failed to replenish them as they expired, letting the supply dwindle to almost nothing. It had 372,000 doses ready to go in Denmark but waited weeks after the first case was identified in mid-May before requesting the delivery of most of those doses. Another roughly 786,000 doses were held up by an F.D.A. inspection of the manufacturer’s new fill-and-finish plant but have now been shipped.

The government also owns the equivalent of about 16.5 million doses of bulk vaccine produced and stored by Bavarian Nordic. But by the time the health agency ordered 500,000 doses worth to be vialed on June 10, other countries with outbreaks had submitted their own orders and the earliest delivery date was October.

Another order for 110,000 doses for European nations soon followed. When the United States came back with two more orders of 2.5 million doses each on July 1 and July 15, the bulk could only be delivered next year.

Mr. Gostin, who now directs the O’Neill Institute for National and Global Health Law at Georgetown University, predicted that President Biden’s decision to appoint two new monkeypox response coordinators would help “light a fire” under federal health agencies. The White House announced Tuesday that Robert Fenton, an administrator at the Federal Emergency Management Agency, and Dr. Demetre Daskalakis, a C.D.C. official, will lead the response.

Mr. Gostin said the nation’s public health agencies have been “kind of asleep at the wheel on this,” and the new coordinators should help with “unblocking all of the obstacles to procuring and delivering vaccines and drugs, which has been deeply frustrating.”

Two senior federal officials, who requested anonymity in order to speak frankly, said Mr. Biden is upset by the vaccine shortage. His administration has often touted its success delivering hundreds of millions of coronavirus shots to Americans, and is stung by criticism that a lack of foresight and management has left gay men — the prime risk group for monkeypox — unprotected.

Some critics blame a failure of leadership at the Health and Human Services Department, saying the department’s secretary, Xavier Becerra, has taken a hands-off approach to an increasingly serious situation. His department not only oversees both the C.D.C. and the Food and Drug Administration, but also runs the Biomedical Advanced Research and Development Authority, or BARDA, which helps develop and buys vaccines, tests and treatments to protect against highly contagious viruses, bioterrorism and other hazards.

During a press call on monkeypox last week, Mr. Becerra said his department is doing all it can to ensure that “we not only stay ahead of this virus but that we end this outbreak.” He noted that he had recently elevated the agency’s Office of Strategic Preparedness and Response so it can respond more quickly to public health emergencies.

Sarah Lovenheim, the department’s chief spokeswoman, said in a statement: “Our response has accelerated to meet evolving needs on the ground, and it will keep accelerating. We will use every lever possible to continue allocating doses ahead of timelines, as possible.”

So far, according to the C.D.C., 6,326 cases of monkeypox have been reported. For now, the virus is spreading almost entirely among gay and bisexual men, and those with multiple or anonymous partners are considered especially at risk. Mr. Becerra noted that while more than a million Americans have died of Covid-19, no one in the United States has died of monkeypox.

The official case count is widely considered an underestimate. Not only is testing limited, but public health officials like Dr. Joseph Kanter, the top medical official in Louisiana, said that monkeypox can be hard to diagnose. “It can be one or two solitary lesions, so if it’s not on a clinician’s radar,” he said, it can be missed.

With too few doses, health officials apparently plan to rely heavily on the “test and trace” strategy that figured heavily in the early stages of the Covid pandemic. As the pandemic escalated, the sheer torrent of cases overwhelmed the ability of health officials to contact people who might have been infected by someone who had tested positive for the coronavirus. Once Covid vaccines became available, they became the cornerstone of the administration’s pandemic response.

Through early June, Health and Human Services officials appeared firmly convinced that the United States had more than enough supply of the monkeypox vaccine, called Jynneos, to handle what appeared to be a handful of cases.

Bavarian Nordic was able to develop the vaccine, which also works against smallpox, largely thanks to the federal government’s backing, which surpassed $1 billion in 2014 and is now edging toward $2 billion. Dawn O’Connell, the federal health agency’s assistant secretary for preparedness and response, told reporters in early June: “The world has Jynneos because we invested in it.”

The company opened a new $75 million fill-and-finish plant in 2021 that is now bottling as many as 200,000 to 300,000 doses a week. At the time, the United States was counting on Jynneos to protect against smallpox, not monkeypox, and the government had a large stockpile of another effective smallpox vaccine. No F.D.A. inspection was scheduled until after the monkeypox outbreak, and it did not conclude until July 27.

In early June, Health and Human Services officials agreed to essentially loan back about 215,000 finished doses of vaccine to Bavarian Nordic so the firm could supply them to European countries that were suffering outbreaks.

“It didn’t make sense while we were waiting for F.D.A. to get the inspection done — which is coming — that we sit on doses that our international colleagues in Europe could actually use,” Ms. O’Connell said on June 10. Now the government is trying to reschedule delivery of those doses for later this year, a company spokesman said.

The final stage of putting the liquid vaccine into vials accounts for a substantial share of the cost of vaccine production. Some federal officials say the health department was slow to submit its orders for that work because officials at BARDA argued they were short on funds.

When the demand for vaccines became an outcry, though, the agency found the money to pay for five million more doses to be vialed. Officials are now contemplating shifting half the work to another firm that may be able to finish and fill doses more than twice as fast.

Some experts say it can take as long as six to nine months for a plant to gear up to handle a vaccine like Jynneos, which contains a live virus in a weakened state. Carlo de Notaristefani, who oversaw coronavirus vaccine manufacturing for the federal government until last year, said that such factories must operate at a high “biological safety level,” including a fully enclosed, segregated manufacturing line.

But he and other experts said it should be possible to streamline the transfer of Bavarian Nordic’s process so another plant could be ready in about three months. A company spokesperson said Bavarian Nordic agreed to pay $10 million of the cost of such a transfer after federal officials said they did not have the budget for it.

Kitty Bennett contributed research.