The Trump administration is proposing to restructure the U.S. Postal Service with an eye to taking it private, a step it said would cut costs and give the financially burdened agency greater flexibility in adjusting to the digital age.

The recommendation is part of a sweeping plan to reorganize and trim the size of the federal government. The broader plan, which would require congressional approval, drew mixed responses on Capitol Hill after it was released on Thursday.

The proposed postal reforms come as shifts in the way people communicate and shop are straining delivery networks created decades earlier to deliver mail across the country. President Donald Trump has launched a task force to review finances and operations at the agency, which has been losing money for years.

Privatizing the Postal Service would provide greater freedom to raise prices and negotiate pay and benefits, according to the White House’s proposal. A private postal operator could cut costs by delivering mail fewer days a week and to more centralized locations, it said, and give the agency access to private capital to fund operational improvements.

The Postal Service has been lobbying for freedom to raise prices and asking Congress to pass legislation to ease some of the burdens of its workers’ retirement benefits. On Thursday, Postmaster General Megan Brennan said she would continue to work with the President and Congress to revamp the agency’s “flawed business model” but it would be up to Congress to determine whether privatizing the agency was the best course.

The American Postal Workers Union, which represents 200,000 postal workers, objected to the idea of privatizing the agency. The proposal “would end regular mail and package services at an affordable cost” and hurt rural Americans and e-commerce, the union’s president, Mark Dimondstein said in a statement.

The Postal Service’s first-class mail revenue is falling as more correspondence and business is conducted by email. At the same time, the rapid growth of e-commerce is pushing greater volumes of packages through its networks, with companies like Amazon.com Inc., United Parcel Service Inc. and FedEx Corp. often relying on the Postal Service’s army of mail carriers for so-called last-mile delivery to people’s homes and businesses.

Parcels are more costly to process and deliver than envelopes. Those expenses, along with wage increases, pension obligations and declining mail volumes, have been weighing on the agency for years. The Postal Service reported a $2.7 billion net loss in the fiscal year ended Sept. 30.

An independent agency of the executive branch, the Postal Service doesn’t currently receive tax dollars for operating expenses, which are funded through sales of postage and shipping services.

President Trump has criticized the Postal Service on Twitter, accusing it of giving a sweetheart deal to Amazon for package delivery and saying the agency needs to be restructured so it can “compete fairly in commercial markets.” The task force he convened in April is expected to issue a report on its findings in August.

“USPS is caught between a mandate to operate like a business but with the expenses and political oversight of a public agency,” according to the White House’s proposal unveiled Thursday.

In her statement Thursday, Ms. Brennan said potential changes to the agency’s business model should be developed and considered by the President and Congress “in an open and transparent manner.”

A privatized Postal Service could be structured like an investor-owned utility and continue to be regulated by the Postal Regulation Commission or another governmental body, “consistent with the existing models of privatization in Europe,” the plan said.

But before going private through an initial public offering or sale to another entity, the agency would have to reform its operations and demonstrate that it could be profitable, the plan said.

Write to Jennifer Smith at jennifer.smith@wsj.com