BOSTON (CBS/CNN) — Massachusetts Gov. Charlie Baker is part of a bipartisan group of governors calling on President Joe Biden’s administration to make changes to the vaccine rollout.  The group expressed concern Monday at the Biden administration’s vaccine rollout, writing in a letter to the White House that better coordination is needed between the federal government and states on distributing doses to prevent confusion and duplicative efforts.

The executive committee of the National Governors Association, comprised of Democrats and Republicans, raised alarm over two areas of confusion: first, the numbers publicly reported by the US Centers for Disease Control and Prevention for vaccine distribution; and second, the separate federal distribution systems — including a recently launched program sending vaccines directly to retail pharmacies — they say have caused inefficiencies.

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The letter amounted to the most explicit call governors have made for the Biden administration to publicly clarify how it is running its distribution process.

Baker said over the weekend that Massachusetts isn’t seeing an anticipated increase of vaccine doses from the federal government. Just over 1.5 million vaccine doses have been shipped to the state in total.

“I can’t stress how important it is for everybody to understand that federal supply is limited,” he said after touring the Springfield mass vaccination site at the Eastfield Mall. “We currently get somewhere between 103 and 106,000 new doses a week. That’s not a heck of a lot more than we were getting a month ago.”

Biden has made distributing Covid-19 vaccines a priority for his first 100 days in office. He has announced new federal purchases of hundreds of millions of doses and has said there will be sufficient supply for most Americans by the end of July.

Yet the letter illustrates the continued confusion over the rollout effort, which began under Biden’s predecessor but that the governors say persists under his watch.

A person familiar with the situation, who asked not to be identified in order to speak candidly, said governors wanted the administration to be more clear with the American public that the constraints in receiving the vaccine are due to a national shortage of doses and not due to the failures of state and local officials, who are largely being blamed.

Governors also want more precise communication from the Biden administration on where vaccine doses are headed, the person said, after running into situations where there are vaccination sites without vaccine doses. States also don’t always know every pharmacy or assisted living facility that’s getting a direct shipment of vaccines from the federal government, further complicating distribution plans, the person familiar with the situation said.

Baker also said Saturday that the state’s inability to see the supply chain is an issue.

“We can only go out one week in terms of or making orders and making decisions about how that vaccine is going to get distributed,” he said.

Some elements of the letter have surfaced on phone calls between governors and the White House, but not to the extent the letter laid out. In this case, governors wanted to make sure the extent of their concerns reached the President.

“We need coordination between the federal government and the state government so we know what pharmacies they’re sending to,” said Gov. Andrew Cuomo, the Democratic governor of New York, during a news conference on Monday. Cuomo is currently embroiled in a scandal over whether figures on nursing home cases in New York State were covered up.

Cuomo, who is the chairman of the National Governors Association and met with Biden at the White House on Friday to discuss vaccination and stimulus efforts, said it was hard to know exactly where the federal government was sending the vaccines doses it is distributing directly.

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“Some pharmacies are already getting a distribution,” he said. “If the federal government is sending to CVS, I don’t send to CVS.”

A White House spokesperson said they are discussing data and reporting issues with the nation’s governors.

“Our strong partnership with states over the last several weeks is helping us vaccinate more people, and we look forward to continuing to be a strong, receptive federal partner as we work with the relevant stakeholders to improve our data and reporting,” the spokesperson said. “Our goal is to get more shots in the arms of Americans as equitably and efficiently as possible, and addressing these issues are critical to doing just that.”

An administration official added that federal agencies, including the CDC, are working to improve the Tiberius system so states have more visibility into what’s happening in their state across the various distribution channels. The official said new upgrades will allow states to see vaccine inventory for retail pharmacy locations, identify where “unaccounted doses” exist and provide an overall view of orders and shipments for all pharmacies and federal entities, along with other improvements.

The letter was also signed by the leaders of Arkansas, Maryland, Alabama, Arizona, New Mexico, Colorado and Michigan.

In it, the governors said discrepancies with the CDC’s public reporting of vaccine statistics were causing “unnecessary confusion” for their citizens. State officials have complained the publicly reported numbers of vaccines allocated by the federal government differed from what was actually on the ground in their states. Both numbers differ from the actual vaccines health care providers have administered into arms.

The governors group said the issues with public reporting of vaccine distribution have been ongoing “since last year,” when the Trump administration was still in place.

“Due to the anxiety created by the demand and supply of the vaccine, it is imperative that the American people fully understand the process,” the governors wrote.

They also voiced concern that the multiple federal vaccination programs — including the pharmacies — are “beyond our control” and confusing for the public.

“If the federal government distributes independently of the states to these same entities without state coordination and consultation, redundancy and inefficiency may very well follow,” the governors wrote.

They singled out federal shipments of vaccines to nursing homes and long-term care facilities, retail pharmacies and Federally Qualified Health Centers as examples of areas where the effort was causing duplicative efforts, writing they were better positioned to know which facilities were equipped to distribute shots.

The Biden administration announced earlier this month it was beginning direct shipments of 1 million vaccines doses per week to retail pharmacies, which it said were selected “based on their ability to reach some of the populations most at risk for severe illness from Covid-19, including socially vulnerable communities.”

Some of the confusion over vaccine distribution stems from the Trump administration’s decision to largely ship vaccine to states and allow them to sort out how to distribute the doses. Rather than reinvent what the former administration put in place, Biden’s team has layered additional distribution channels on top of state vaccine allocations, which has, in some ways, made the process more complicated.

Governors are also confronting a problem that’s partly of their own making. Many governors opted to make vaccine doses available to the elderly even when it was clear that supply was going to be extremely limited.

The Trump administration also encouraged states to open up vaccine eligibility in order to get shots in arms more quickly. Now those broad categories of eligibility are breeding frustration as elderly Americans or those with preexisting conditions find out that they are eligible for a vaccine but none is available.

(© Copyright 2021 CBS Broadcasting Inc. All Rights Reserved. CNN’s Kevin Liptak and Sara Murray contributed to this report.)

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