Congress moved one step closer Wednesday to overhauling the cash-strapped U.S. Postal Service by approving sweeping reforms to rebalance the mail agency’s finances and help cut the size of its delivery network.

The bipartisan measure passed 62 to 37 and would give the cash-strapped Postal Service nearly $11 billion to offer buyouts and early retirement incentives to hundreds of thousands of postal workers and to pay off its debts. Revised estimates on how much the Postal Service owes to federal worker pension accounts have determined that the agency has overpaid its obligations to the fund over several years.

The measure also would permit the end of Saturday mail deliveries in two years and only after USPS determines it is financially necessary. The Postal Service also could move forward with plans to shutter thousands of post offices and hundreds of mail distribution centers — but senators placed several restrictions on when, where and how outposts in rural communities could be closed.

The bill also modifies mail service standards to ensure that the Postal Service preserves the overnight delivery of mail sent to nearby communities, but allows USPS to slow the delivery of mail destined for destinations farther away.

In a statement, the Postal Service said it was disappointed with the Senate bill because it falls short of its cost-cutting plans. Citing its cash shortfalls, the USPS said it was “inappropriate” to expect it to keep unprofitable facilities open longer than needed.

The Postal Service has warned for years that it is on the verge of financial collapse and can no longer sustain operating a delivery network that processes 554 million pieces of mail each day. Agency leaders hope to cut more than $22 billion in costs by 2015 as the popularity of traditional mail declines. Letter carriers delivered 168 billion pieces of mail last year, down from 202.8 billion delivered a decade ago, according to postal figures.

Senators have worked for more than a year to give the USPS the ability to set postage rates and delivery schedules and to determine the fate of unprofitable post offices free of congressional intervention, but senators eager to protect home-state interests added restrictions, including one barring USPS from closing a rural post office unless the next-nearest location is no more than 10 miles away.

Senate Majority Leader Harry M. Reid (D-Nev.) called the bill’s passage a “very important day for the American people” and praised senators for considering 39 amendments over two days in bipartisan fashion.

“It’s going to be something that will send the House a message — that we can do big things,” Reid said.

But Rep. Darrell Issa (R-Calif.), lead sponsor of a competing postal reform measure in the House, called the Senate bill “wholly unacceptable” because it delays the Postal Service’s ability to quickly close unprofitable post offices and processing centers.

“While the Postal Service is actually trying to shutter some facilities it does not need, the bill forces the Postal Service to keep over 100 excess postal facilities open at a cost of $900 million per year,” Issa said.

Issa’s bill, which has not been scheduled for a vote in the House, would allow the USPS to end Saturday mail deliveries, streamline postage rates and require postal workers to pay the same health insurance premiums as federal employees. It also would establish a financial control board to overhaul postal finances and a create a commission that would recommend which postal facilities should be closed.

Business groups that rely on mail remain hopeful Congress will strike a deal before May 15, when the Postal Service plans to resume closing post offices and processing facilities.

“I’m surprised the Senate is moving a postal bill in an election year, and pleased they’re getting the ball rolling,” said Tony Conway, head of the Alliance of Nonprofit Mailers. His group supports efforts to end Saturday mail delivery and to close post offices and processing plants.