By Alexa Corse and Natalie Andrews

WASHINGTON -- House Democrats set a Saturday vote on a bill that would prohibit operational changes to the Postal Service until well after the election and give $25 billion in additional funding to the agency, which has become the focus of a political battle over expanded mail-in voting that Democrats favor amid the pandemic and President Trump has continued to disparage.

Democratic lawmakers have also called the leaders of the U.S. Postal Service to testify before Congress next Monday about their concerns over mail delays and cost-cutting moves being made by Louis DeJoy, the new postmaster general and a major Republican donor, amid persistent budget shortfalls. Mr. DeJoy and Robert Duncan, chairman of the Postal Service board of governors, said they would attend.

The Postal Service has said it can't promise to deliver all ballots in time to be counted if they are mailed close to Election Day and has urged election officials and voters not to leave mail-in balloting until the last minute. The agency and some election officials say some states allow voters to request absentee ballots so late that it is difficult to guarantee their delivery in time to be counted.

House Speaker Nancy Pelosi (D., Calif.) told Democrats in a letter that she is bringing lawmakers back to Washington from their August recess, saying Mr. Trump is on a campaign to "sabotage the election by manipulating the Postal Service to disenfranchise voters," citing operational changes at the Postal Service that postal-union representatives and some customers say have delayed mail.

The legislation appears unlikely to be taken up by the Senate, which is on recess until September. "The Postal Service is going to be just fine, " Senate Majority Leader Mitch McConnell (R., Ky.) told reporters on Monday. "We're going to make sure that the ability to function going into the election is not adversely affected."

As part of recent negotiations with Democratic lawmakers, White House spokeswoman Sarah Matthews said Monday, Mr. Trump offered $10 billion for the Postal Service on top of a $10 billion line of credit that Congress previously authorized in March.

Mr. McConnell also said Monday he supported $10 billion to help the Post Office. As the GOP-controlled Senate is on recess and Mrs. Pelosi is backing $25 billion, legislation concerning $10 billion in funding isn't likely to move soon.

White House Chief of Staff Mark Meadows told reporters on Air Force One on Monday that Mr. Trump is open to more funding for the Postal Service as part of broader negotiations on the coronavirus relief bill. Talks between Democrats and Republicans on the next phase of legislation have been stalled for more than a week.

On Fox News Monday morning, Mr. Trump called Mr. DeJoy, a Trump campaign donor and former logistics-company executive who took over as postmaster general in June, a "very good business guy." Mr. Trump says he opposes mailing out ballots to all voters, a process he says would invite fraud and errors, but is fine with individual voters being allowed to request a mailed ballot in advance of the election.

During a campaign event in Minnesota on Monday, Mr. Trump railed against mail-in ballots, distinguishing them from absentee ballots, which he himself uses in Florida. The state of Florida, however, calls its process vote-by-mail, not absentee.

"Absentee ballots are good. You send for the ballot, you're not going to be in your state, and you get it back and you do something.... It's a process, you have to work for it a little bit," he said. "But these ballots they want to send them out in some states...they want to just have millions of ballots."

Most states will allow voters to cast a mailed ballot even if they aren't going to be out of town in November. A smaller number of states require that voters meet specific criteria to vote absentee.

Researchers haven't found evidence of widespread fraud linked to by-mail ballots, although some isolated cases have been tied to the practice. A different problem is that some states and counties have limited staffing and technology to deal with a surge of mailed ballots, which created logistical problems for some voters during recent primaries in New York and elsewhere.

The House bill, introduced by Oversight Committee Chairman Rep. Carolyn Maloney (D., N.Y.), prohibits the Postal Service from implementing any changes to operations or service levels it had in place on Jan.1 until the end of the Covid-19 emergency or Jan. 1, 2021, whichever comes later.

The bill forbids the closure or consolidation of any post office or reduction of facility hours, ending overtime pay for workers, or any other measure that would prevent the Postal Service from meeting its service standards, delay mail or increase the volume of undelivered mail.

Democrats are also adding $25 billion for the Postal Service to the legislation, according to a Democratic aide. That is the amount the Postal Service's board of governors requested in April to cover operating costs and extra expenses incurred during the pandemic.

Republicans objected to the House holding a vote on such legislation before hearing from Messrs. DeJoy and Duncan about Postal Service operations.

"Generally, I would think we would want to make sure what we were going to do was going to fix the problem," said Rep. Fred Keller (R., Pa.), a member of the Oversight panel. "It's almost like ready, fire, aim."

Mr. DeJoy has moved to curtail costs since taking over as postmaster general, including having trucks leave on time and limiting overtime by targeting what senior postal officials have called unnecessary costs and lateness.

His efforts have come amid some other changes that the Postal Service said were routine and not tied to Mr. DeJoy's arrival, like planning the removal of some mail-sorting machines or mailboxes, which the Postal Service said was in response to declining mail volumes. Amid the recent outcry, Postal Service spokeswoman Kimberly Frum said the agency would postpone routine removal from streets of seldom-used mailboxes for 90 days.

Earlier this month, Mr. DeJoy told a Postal Service board of governors meeting that the agency "has ample capacity to deliver all election mail securely and on time in accordance with our delivery standards."

A lawsuit filed Monday in Manhattan federal court contests that. Several Democratic politicians and other voters sued Mr. Trump, the U.S. Postal Service and Mr. DeJoy to ensure the agency has sufficient funding. "President Donald J. Trump and his newly appointed Postmaster General Louis DeJoy have set about to ensure USPS cannot reliably deliver election mail," the plaintiffs argued in the filing.

Asked about the lawsuit, White House spokeswoman Sarah Matthews said: "Politically motivated lawsuits are not rooted in giving Americans the power of the vote."

A spokesperson for the USPS didn't respond to a request for comment.

Republicans have largely dismissed Democrats' concerns over mail-in voting, but some Republican lawmakers have raised concerns over postal-service delays.

"The Democrats' wild and baseless conspiracy theory about the United States Postal Service is irresponsible and only undermines the American people's faith in the integrity of the election and our institutions," Rep. James Comer (R., Ky.), the top Republican on the House Oversight Committee, said Monday.

Still, Sen. Susan Collins (R., Maine) on Sunday evening called for the Senate to reconvene to consider her bill -- co-sponsored by Sen. Dianne Feinstein (D., Calif.) -- that would provide the Postal Service with up to $25 billion.

The Postal Service faces long-running financial problems due to legislative requirements, including that it prefund retiree medical benefits. Its other challenges include a steep decline in first-class mail, its most profitable service, amid the growth of digital communication. But it has said in financial filings that it has enough liquidity to fund operations through at least August 2021. The Postal Service reached an agreement for a $10 billion loan from the Treasury Department in July.

The Postal Service has said its financial condition won't affect its ability to process and deliver election mail. The agency has recommended that voters mail back their ballots no later than a week prior to their state's due date, but many election officials recommend doing so even earlier if possible.

--Gordon Lubold and

John McCormick

contributed to this article.

Write to Alexa Corse at alexa.corse@wsj.com and Natalie Andrews at Natalie.Andrews@wsj.com