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In a phone call with the four-star Army general overseeing the distribution of coronavirus vaccines, Tennessee’s top health official laid out what she saw as the No. 1 obstacle to getting more shots into people’s arms.

“The only limitation is supply,” Health Commissioner Lisa Piercey recalled telling the general, Gustave F. Perna, earlier this month.

From Miami to Manhattan, hospital leaders and public officials have been equally emphatic. But in one of the most puzzling aspects of the early vaccine rollout, the shortages are intensifying in some jurisdictions, while others have yet to use all their vaccine. The bottleneck isn’t just in administering the vaccines; some states are not ordering everything they’ve been allotted.

The result is widespread confusion about how much vaccine is available from one week to the next, and how much supply states actually need to inoculate residents in priority groups. Both areas of confusion are barriers to the national immunization campaign that President Biden pledged to mount in his first days in office.

The president’s advisers have said they were left no plan by the Trump administration. But what they inherited this week was more like a black box than a bare cupboard — the result of fractured communication among federal, state and local officials and a juggling act between manufacturers making a new product and thousands of providers, from big hospital systems to tiny clinics, struggling to plan around an unknown amount of vaccine.

“We don’t have the visibility that we would hope to have into supply and allocations,” Jeff Zients, the Biden administration’s coronavirus coordinator, acknowledged in a Wednesday briefing.

The delays in ordering and distribution have many causes, including uncertainty about vaccine supply and the status of second doses as well as the hesitancy of some people to get the shots. Also at issue are the logistical hurdles of performing immunizations in long-term-care facilities and the ultracold storage requirements and batch size of the product developed by Pfizer and German company BioNTech. That vaccine, one of two authorized for emergency use in the United States, comes in a minimum order of 975 doses. Once vials are opened, doses must be used within six hours.

Health-care workers across the U.S. received their first dose of the Pfizer-BioNTech coronavirus vaccine following its Dec. 11 authorization by the FDA. (The Washington Post)

Perversely, limited supply is sometimes the obstacle to faster distribution, health officials say, because there is reluctance to set up vaccination sites and mobilize beleaguered medical workers only to perform a meager number of inoculations.

Kentucky’s public health commissioner, Steven J. Stack, likened apportioning limited supply to sprinkling “pixie dust” across his state.

“The people who are willing to give it and administer it don’t get enough of it to plan their staffing and their operations and to tell the public when they’re likely to be able to provide it,” he said.

Asked why federal and state officials often give conflicting accounts about supply, Anthony S. Fauci, a top Biden adviser and director of the National Institute of Allergy and Infectious Diseases, said Thursday at a White House briefing, “I don’t know the answer.”

David Kessler, a top Biden adviser who now leads the federal government’s vaccine accelerator effort, has made few immediate changes to how vaccines will be allocated to 64 jurisdictions and five federal agencies. The new administration has vowed to set up federally run mass vaccination sites but does not anticipate new federal allocations, instead drawing on supply already made available to states, according to an administration official who spoke on the condition of anonymity to discuss ongoing deliberations.

Zients said there was not yet a decision on whether to move ahead with a change announced by the Trump administration to give slightly more vaccine to states with larger elderly populations, to encourage immunization of adults 65 and older, along with front-line workers.

He said his team has heard “over and over” from governors about the need for more precise projections on vaccine supply, but state health officials are quickly recognizing that this expectation is not realistic.

“Please know we’ve never promised a steady stream of vaccine to anybody, even to ourselves,” Mississippi’s top health official, Thomas Dobbs, said Thursday.

Of Biden’s promise to shift Trump’s strategy, Dobbs said all the state has heard are “rumors of rumors of rumors.”

The pace of vaccine administration became politically charged in recent weeks as Biden’s advisers blamed the sluggish national rollout on the Trump administration, which in turn pressured states to dispense their supplies more quickly and held up certain states, such as Florida, as examples. Last week, the outgoing administration proposed rewarding states giving shots at a rapid clip with additional doses, a system Biden officials say they will scrap.

The situation deepened anxiety among providers and state officials about requesting doses that might ultimately go unused, potentially endangering their future supplies.

“I don’t want to be the small practice responsible for wasting a valuable resource,” said Macdonald M. DuBose, a geriatric medicine specialist and the chairman of the South Carolina Medical Association.

That some jurisdictions aren’t ordering all available vaccine while others beg for more goes to the heart of the disjointed immunization effort underway in the United States. It also helps explain why the federal government has liquidated its reserve of second doses at the same time that Pfizer maintains it has millions of doses in reserve — as many as 5 million by the end of last week, or about 25 percent of what had been made available to the United States at that point, according to former federal officials.

Those are not doses earmarked for booster shots, according to multiple people knowledgeable about the process, some of whom spoke on the condition of anonymity because they were not authorized to address it. Rather, those are doses that have accumulated week after week because some states are not ordering up to their limit or are putting aside a set amount of their vaccine supply for purposes including inoculations in nursing homes or mass vaccination clinics.

Ordering limits are set for states twice a week, on Thursday and Sunday. They reflect updated allocations, so the actual number of unclaimed doses is a moving target. The ordering is spaced out both to ease the burden on distributors and to help states distinguish between first and second doses, with priority given to the latter.

As of early this week, states not ordering up to their limits included Illinois, Kansas, Mississippi, Nevada, South Carolina and Texas, according to Michael Pratt, a former Health and Human Services spokesman. Data compiled by the Centers for Disease Control and Prevention indicates the fewest doses per capita have been distributed in Nevada, South Carolina and Texas. By the end of the week, Mississippi had ordered all the vaccine available to the state, officials said.

The discrepancy is so glaring in South Carolina that the public health director, Brannon Traxler, affirmed Wednesday that the state is receiving its “fair and appropriate allocation.” She was responding to concerns that South Carolinians were being shortchanged in favor of people in other parts of the country.

The reason so much of South Carolina’s allocation has gone unused, she said, is that the state had set aside the entire amount needed for long-term-care facilities rather than parceling that out in increments, as other states have done. CVS and Walgreens pharmacies are handling immunizations at long-term-care facilities as part of a federal partnership, which has been slow to get off the ground in some places. Maine recently redirected nearly 2,000 doses from Walgreens to two hospitals because the pharmacy had no immediate plans to administer the shots, according to state officials.

But doctors and public health experts said the supply problems in South Carolina and elsewhere go beyond the need to stockpile doses for nursing homes.

DuBose said too few providers have the cold-storage capacity for Pfizer’s product. He also said communication from the state and the federal governments has been inadequate, both in identifying who is eligible for vaccination and persuading those people to take the vaccines.

“There’s just an assumption that this is something everybody is going to wait hours in the rain to receive,” he said.

Mixed messages about the status of second doses, meanwhile, created uncertainty about supply, said Harris Pastides, an epidemiologist and former president of the University of South Carolina who advised the state on earlier phases of its pandemic response.

The Trump administration was never clear about whether states were supposed to maintain reserves of second doses, he said, especially as Britain began to experiment with spacing out the doses to deliver some protection to more people more quickly.

When federal officials announced last week that they were no longer maintaining a stockpile at the national level because of increased confidence in manufacturing — not because they were changing the approach to second doses — they led states to believe they would see a windfall in supply. It turned out that much of the reserve had already been shipped out, making it all the more difficult for state and local officials to instill confidence in their populations that there would still be enough for booster shots.

Melaney Arnold, a spokeswoman for the Illinois Department of Public Health, pointed to confusion over the release of second doses and said the gap between what was available to the state and what it had ordered would be eliminated “as more residents become eligible for second doses and our providers put in those orders.”

Officials in other states, including Texas, said they had already increased their orders substantially and were mystified by federal figures showing their allotments not being fully distributed.

The only time Texas ordered less than its full allotment was during the week of Christmas, when Moderna doses were first shipped to the states, said Chris Van Deusen, a spokesman for the Texas Department of State Health Services. The next week, he said, “we pulled that down and haven’t done that since.” The state places its orders several days each week, said Van Deusen, suggesting that the full scope of its requests may not be immediately clear to federal officials.

To add to the confusion, starting next week, each state’s allocation will reflect an updated number of doses contained in each Pfizer-BioNTech vial — six instead of the current five. Given Pfizer’s packaging, that means the minimum order will be 1,170 doses instead of 975.