The District’s mayor and the governors of Virginia and Maryland will meet Aug. 28 to discuss Metro amid hopes that they will start to narrow the wide gap that separates them over how to fund the transit system.

Virginia Gov. Terry McAuliffe (D), Maryland Gov. Larry Hogan (R) and District Mayor Muriel E. Bowser (D) will hold their first regional summit on Metro in 10 months and may discuss other issues as well, officials said.

The meeting, to take place at Mount Vernon, comes at a critical time for the transit system. The region is struggling to agree on how to handle Metro’s request to raise at least $500 million a year in additional revenue that the agency says it needs for new equipment and maintenance to restore the system to a state of good repair.

Metro’s supporters in Virginia and Maryland say they need to reach consensus by the end of the year on a funding plan to win necessary approval when the two states’ General Assemblies convene in January.

Bowser has repeatedly called for a regionwide, penny-per-dollar sales tax for Metro, but McAuliffe and Hogan have resisted the levy for separate reasons.

Hogan, an outspoken opponent of new taxes, has ruled out raising taxes statewide to obtain extra money for Metro. But he has left open the possibility that the two Maryland counties served by Metro — Montgomery and Prince George’s — might tax themselves to support the transit system.

McAuliffe is willing to consider tax increases but says Metro must first demonstrate progress on safety, reliability and efficiency.

The Virginia governor has little leverage, as he steps down in January. He recruited former U.S. transportation secretary Ray LaHood to study how best to fund and reform Metro, and LaHood plans to issue a report with recommendations in September.

The two governors and the mayor are expected to hear an update on LaHood’s progress at the August summit.

The three have not fixed a specific agenda for the session yet, but Metro will be a main topic, according to officials from all three jurisdictions.

McAuliffe is hoping for “a constructive dialogue” on Metro to make progress toward an agreement on reforms and funding, spokesman Brian Coy said. That would help persuade the ­Republican-dominated legislature in Richmond to overcome its skepticism about backing Metro.

“Of course he wants us all to be on the same page,” Coy said. “The issues remain the same, particularly with our General Assembly. They’re going to need to see further evidence that the money we’re already spending is being used wisely, with respect to safety and performance.”

Bowser’s chief of staff, John Falcicchio, said the mayor still supports the regional sales tax but is open to other funding methods as long as they provide a steady, reliable stream of revenue.

“The mayor has always said it was important to find dedicated revenue before the end of 2018, to make the critical investments that Metro needs for safety, reliability and capacity,” Falcicchio said.

“What others put on the table, we’re open to, as long as it’s a dedicated stream of revenue,” he said.

Hogan spokeswoman Amelia Chasse confirmed the Metro summit would take place and noted that the Maryland governor has advocated for increased federal funding for the transit system.

Metro is the only major transit system in the country that does not obtain a significant amount of funds from a tax or other dedicated source. Potential revenue sources, other than a sales tax, include new property taxes or fees.

Northern Virginia Republicans have also proposed restructuring existing funding sources — such as from property taxes — into dedicated streams that could be used to float bonds and thus increase Metro’s borrowing capacity.

Bowser recently urged a large gathering of church-based activists who support greater public funding for Metro to lobby legislators in Virginia and Maryland.

“We [in the District] don’t believe in cutting service and raising fares,” but Richmond and Annapolis see things differently, Bowser said July 26 at a meeting of 400 members of the Washington Interfaith Network.

“I hope they come along,” she said. “I need you to go to Richmond, because that’s where the decision is being made.”

Later she said lobbying was needed in Maryland, as well.