Washington (CNN)The Trump administration is winding down its effort to expedite critical medical supplies from overseas, known as "Project Airbridge," in the coming weeks, US Navy Rear Admiral John Polowczyk told reporters Friday.

       President Donald Trump repeatedly heralded the initiative, calling it an "amazing success." But over time, the effort became a point of contention between the Trump administration and states desperate for supplies because of limited visibility into how many supplies came in and where they were ultimately going. Its success, therefore, has been difficult to measure.

       "We are looking at a process to ramp down the Airbridge as we go through May into June. We believe we've gotten the volume that we've needed to effectively, what I call, prime the pump to get more supplies here to beat the ocean-going method," Polowczyk said, adding that there may be items needed in the future that they'll consider flying in on an individual basis.

       Inside 'Project Airbridge,' the US effort to bring medical supplies from overseas

       The volume of supplies, cited by Polowczyk, includes all the ways personal protective equipment has been procured by the federal government and the private sector, combined, according to the Federal Emergency Management Agency.

       In late March, FEMA worked with six major medical distributors to shore up supplies in the US by helping the companies bring in equipment abroad at a faster pace on chartered flights, which average between $750,000 to $800,000 a flight, and then directing a portion of those supplies.

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       But while the supplies are flown in by FEMA, the allocation of supplies is split between the administration's designated hotspots and the distributors' customers, some of whom might also be in those critical areas.

       FEMA has not provided details on allocation or prioritized hotspots, though, in recent weeks, states began receiving breakdowns of where supplies were delivered.

       "Every week, we provide a report to every state, to the governor, of how much the distributors have provided to their state, down to the county level," Polowczyk said Friday. "They have great visibility on what this network is providing to their states."

       But not all states agree the program has been a success.

       Illinois Gov. J.B. Pritzker, a Democrat, has been vocal in his criticism of the program.

       "What they are taking credit for, the White House, is that the distributors have customers in Illinois that they are sending goods to because those customers ordered those items of PPE, so that's a far cry from delivering to the states so that we can distribute," Pritzker said.

       Lawmakers have also sought details on the program, which has largely been shrouded in secrecy.

       As of May 13, the administration has conducted 139 flights to bring in millions of supplies, including respirators, gloves, surgical gowns, and face shields, according to FEMA Administrator Pete Gaynor.

       While Project Airbridge is not the only federal endeavor to bolster supplies -- the departments of Defense and Health and Human Services are also assisting -- the initiative is one of many tests of private and government partnership at a critical time, but that type of partnership was not the original idea.

       The framework was originally conceived in late March by an assistant professor at the Massachusetts Institute of Technology and member of the Covid-19 Policy Alliance amid growing concerns over supply shortages.

       The proposal, put together by Valerie Karplus and first reported by the Washington Post, outlined how employing US passenger and freight aircraft to bring in supplies would shorten the time it takes for them to arrive.

       "Within four weeks, with doubled aircraft capacity relative to pre-virus levels and additional production ramp up in China, we could meet 50% of projected U.S. demand for masks and suits," the memo reads.

       Karlpus sent the memo, titled "Proposal: A Medical Supply Airlift to Protect the U.S. from COVID-19," to airlines, lawmakers, and the administration.

       "I spoke by phone with Admiral Polowczyk and we talked in detail through the elements of the plan and he sounded really receptive," she said. Five days later, Karplus learned the plan was being put in motion, but the allocation of product would be done by distributors, instead of the federal government working closely with states.

       As Airbridge winds down, administration officials recognized a need to bolster domestic manufacturing of medical equipment. Similarly, states have doubled down on efforts to make more supplies in the United States in an attempt to become less dependent on the international market.

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