(Reuters) -- The Senate advanced legislation Wednesday evening that would let the U.S. Postal Service end Saturday mail after two years as part of efforts to overhaul the agency and keep it from shuttering thousands of facilities next month.

The Postal Service has been losing billions of dollars yearly due to the rise of online communications and high labor and other costs. Both houses of Congress have been working for months on legislation to restructure the agency and offer some relief.

The Senate voted 62-37 to pass its bill, which would also let the mail agency use about $11 billion in surplus funds in a retirement account to offer early retirement incentives as a means to reduce its workforce.

But while the bill was sponsored by a bipartisan coalition of senators, it faces a difficult challenge in the Republican-led House of Representatives. Leaders have yet to schedule a full House vote on the leading bill, which differs significantly from the Senate version, even though a committee approved it in October.

This bill will bring the change that the post office needs to stay alive and serve the people and businesses of our country, independent Sen. Joe Lieberman of Connecticut, one of the Senate bill's sponsors, said before the vote.

This great American institution, which still delivers over 560 million pieces of mail every day and helps to support 8 million jobs throughout our economy, cannot be allowed to spiral downward into bankruptcy, he said

Now we've got to challenge the House to pass a bill, he told reporters afterward.

The Postal Service lost more than $3 billion last quarter, much of it due to a massive annual payment for future retiree health benefits. Postmaster General Patrick Donahoe has said the agency needs to cut operating costs by $20 billion by 2015, including ending Saturday mail delivery, taking over its health care plan and raising postage rates beyond inflation.

The agency also intends to close thousands of money-losing post offices and hundreds of mail processing facilities.

Postal officials agreed late last year to a moratorium on closings through mid-May to give Congress time to pass legislation. The Senate bill would place some restrictions on which facilities can be closed, requiring the Postal Service to consider factors such as Internet access before closing a post office.

The final version of the bill also forces the Postal Service to keep some post offices open until after November elections to protect by-mail voting and to maintain rural post offices that are more than 10 miles away from another location.

Although senators disagreed on how much protection to offer rural post offices, they did agree on one point: They approved an amendment by Sen. Rand Paul, R-Ky., that would close five of seven post offices in the Capitol.

Fredric Rolando, president of the National Association of Letter Carriers, called the bill flawed in a statement on Wednesday and said the group would continue to fight for a postal overhaul that would eliminate the annual retiree health payment and not allow the agency to end thousands of jobs.