Two D.C. fire department ambulances caught fire Tuesday — one in a hospital parking lot, the other on an emergency call — more blows to an agency that is under criticism as it struggles to quickly reach patients and cope with staff shortages.

No injuries were reported, and the fires, both starting in the engines, were quickly extinguished. One fire occurred shortly after 4 p.m. outside MedStar Washington Hospital Center in Northwest Washington. Earlier, an ambulance caught fire outside a home on Benning Road in Southeast Washington; the patient, who was still inside the home, was taken to a hospital in another ambulance.

A photograph of the burning vehicle on Benning Road that was posted on the fire union’s Twitter account provided a stark image of what labor leaders say is a poorly maintained fleet. The D.C. inspector general has criticized the fleet’s maintenance, as has the chairman of the D.C. Council’s public safety committee.

“Unfortunately, there’s no bottom,” said Edward C. Smith, president of Local 36 of the D.C. firefighters union.

While Smith cautioned that what caused the fires remains undetermined, the fact that they started in the engines leads him to think a malfunction was the cause in both cases.

This burning ambulance was on a call Tuesday morning on Benning Road in Southeast Washington. The cause of the fire is under investigation. (Courtesy of D.C. Firefighters Local Union 36)

“It’s the state of our fleet,” Smith said. “We’ve been sounding the alarm for two years, and we’re seeing one failure after another.”

Tim Wilson, a spokesman for the D.C. Fire and Emergency Medical Services Department, said he was at a loss to explain the fires or how they started.

Fire officials say they are trying to address various problems in the department. They hired a private consultant for $182,000 to audit the fleet after the inspector general found that they had lost track of reserve vehicles, listing many fire engines as ready for duty when they had, in fact, been stripped and sent to scrap yards.

After more than 60 ambulances had mechanical issues last month, including many with broken air conditioning during a heat wave, the department was forced to contract with a private ambulance company to staff Washington Nationals baseball games.

But top fire officials have accused the rank and file of contributing to the breakdowns and staffing shortages through neglect or incompetence, such as when an injured D.C. police officer and a heart attack victim had to wait to be taken to hospitals. The fire union blames the problems on bad management and inadequate staffing.

Another embarrassment for the agency occurred Thursday when a D.C. ambulance assigned to President Obama’s motorcade ran out of gas and was left stranded on the South Lawn of the White House. The incident was first reported by the Washington Times and WJLA-TV.

Smith, the union president, said that drivers had reported last year in an internal log and to commanders that the vehicle’s fuel gauge was faulty but that it never got fixed. He called the incident a “national embarrassment” and emblematic of poor upkeep.

But fire officials denied knowing about a broken gauge and said it appears that the driver failed to fill the tank.

“It is a clear example that people aren’t consistent with the performance of their duties,” Wilson said. “That definitely poses a problem for the administration in this fire department.”