WASHINGTON — A push by District of Columbia Mayor Muriel Bowser to fund the struggling Metro subway system with a new regional sales tax got a cool reception Wednesday from the governors of Maryland and Virginia.

During a discussion sponsored by business groups, the Democratic mayor drew applause when she said the region needed to agree on a tax, possibly as low 0.5 percent on retail sales, to give Metro the money it needs to serve a growing population. But Republican Gov. Larry Hogan of Maryland and Democratic Gov. Terry McAuliffe of Virginia said they would not commit to giving Metro more money until the system improves.

“You can’t throw good money after bad, but we’ll continue to invest in things that make sense,” Hogan said. “This is, unfortunately, a system that has appeared to be broken for a long time.”

Metro, the nation’s second-busiest transit system, is the only large transit network in the U.S. without a dedicated revenue stream. The District, Maryland and Virginia subsidize the system’s operating budget, but for Metro to get more money, those jurisdictions — including local governments in northern Virginia — all have to agree.

Ridership on the system has slipped amid an alarming series of breakdowns, including a January 2015 fire that caused a train to fill with smoke inside a downtown Washington tunnel, killing one passenger and sickening dozens more. Fires on the tracks, often caused by faulty or contaminated insulators protecting the third-rail power cables, have been a recurring problem, and Metro is in the midst of a nine-month maintenance blitz, with sections of track being shut down for weeks at a time.

McAuliffe said Metro needs to meet concrete goals for safety and reliability before seeking more money.

“They’ve got to get through a couple hoops first, to get us to where we need to be to say we’re going to be throwing money at this,” McAuliffe said.

Regional business leaders have pushed for the dedicated tax, citing Metro’s importance to economic development. The Metropolitan Washington Council of Governments sent a letter to the governors and mayor on Wednesday asking them to give Metro a “secure and solid financial foundation.”

Metro has also curtailed late-night service, a move that has angered elected officials and caused headaches for riders who hope to attend Washington Nationals playoff games. With the system closing at midnight, fans at Thursday’s 8 p.m. game face the possibility of having to leave early if they want to ride Metro home.

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