D.C. police arson detectives have launched a criminal investigation into Tuesday’s ambulance fires amid a deteriorating labor dispute between firefighters and the city that raises new questions about safety.

The probe comes as concerns mount over frequent break-downs of fire department vehicles, which contribute to slow response times. City officials previously have blamed mechanical troubles on workers’ poor performance and negligence.

On Wednesday, Paul A. Quander Jr., the deputy mayor for public safety, said he requested that police look into the fires “to be certain that nothing untoward is occurring to these vehicles that could possibly put the public at risk.”

Union officials took umbrage at his use of the word “untoward,” saying it appears that firefighters and paramedics are being accused of sabotaging equipment to exaggerate their allegations of management incompetence.

Quander declined to elaborate on what he meant. But his comments — and his decision to elevate a department inquiry into a police matter — fueled more harsh rhetoric in the poisonous relationship between the labor group and city leaders.

The ambulance had been 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)

The deputy mayor said it’s unusual for the engines of two ambulances to catch fire hours apart. He said that the fires “raised concerns for me” and that he wanted to make sure there were not “other issues at play” aside from mechanical problems.

“I’m not going to speculate,” Quander said. “I want to be guided by the facts.”

D.C. Council Chairman Phil Mendelson said the fire department “is becoming an embarrassment to the city,” adding that there must be “a lot of citizens who think there is a meltdown going on.”

In an interview, Mendelson (D) declined to assess blame, saying the “downward spiral” is a result of increasing labor tensions and a demoralized workforce, in which he said jobs at all levels “are not being done as carefully as they need to be done.”

The chairman said that “with the deputy mayor’s involvement, the citizens are safe.” Asked whether residents are safe with the embattled fire chief, Kenneth B. Ellerbe, Mendelson responded, “I said what I said.” He noted several crises that he said Quander stepped in to resolve.

Mendelson declined to say whether Ellerbe should resign, but he said, “I think the chief has to get control of the department.”

Ellerbe was traveling and not available for comment. But he told WTTG (Channel 5) on Wednesday that the department is “in a critical period of change” and that he has been “working hard behind the scenes” to address the problems.

Tuesday’s fires occurred while the ambulances were on calls, one idling outside a patient’s home in Southeast Washington, the other outside a hospital emergency room in Northwest. A fire department spokesman said Wednesday evening that the latter fire might have started in an air compressor but a final determination had not been made.

Last Thursday, an ambulance assigned to President Obama’s motorcade — Medic 1 — ran out of gas and was left stranded on the south lawn of the White House.

These latest incidents proved potentially dangerous and embarrassing but also emblematic of the union-management standoff.

In the case of Medic 1, either the city failed to heed a warning of a broken gas gauge, as the union says, or paramedics failed the most basic of tasks — to fill the ambulance with gas — before a mission to protect the president.

“Chief Ellerbe gets blamed for a lot of things,” Quander said. “He was out of town, and he’s not responsible for putting gas in ambulances.”

Edward C. Smith, president of firefighters’ union Local 36, said the labor group welcomes an outside investigation into the fires and called on the National Transportation Safety Board to conduct a broader review of the department’s fleet. In a statement, Smith lashed out at Quander, saying the “only thing untoward behind these ambulance fires is the complete neglect by those in charge.”

The labor leader said any suggestion that members are responsible for recent mishaps was unfounded. In an effort to demonstrate what he said “firefighters are forced to try and work with on a daily basis,” he sent out a statement that included a picture of a parking sign jammed into an ambulance engine “as a makeshift heat shield.”

The fire department said that aluminum signs were put in engine compartments of some ambulances to fix problems with air conditioning. They are being removed, officials said. Neither ambulance that caught fire Tuesday had the signs.

The dispute, rooted in long-stalled labor talks, heightened in January when one-third of the firefighters on duty for New Year’s Eve called out sick, and a man suffering a heart attack died after a delay getting him to a hospital. The union denied claims by the city of orchestrating a sick-out.

A string of failures followed, including delays in getting help to an injured D.C. police officer and the breakdown of an ambulance transporting a man who had been shot by police. The city had to outsource ambulance service to Nationals games when air conditioning failed in dozens of vehicles during a heat wave. And the city routinely operates with a deficit of paramedics — a problem the union blames on unfilled vacancies and the city blames on unscheduled absences.

D.C. Council member Mary M. Cheh (D-Ward 3) has called on Ellerbe to resign, and the head of the public safety committee, Tommy Wells (D-Ward 6), who is running for mayor, said he would not keep the chief if elected. Last month, Wells’s committee shot down Ellerbe’s ambulance redeployment plan, which the chief said would improve response times.

Wells and Ellerbe sparred during a hearing in March over the quality of the department’s vehicles after a report by the D.C. inspector general found many vehicles in the reserve fleet were in disrepair.

The report also said investigators had heard allegations of sabotage dating to 2011 that included slashing of tires, tampering with air conditioners and intentionally driving ambulances in low gear to burn out transmissions in a dozen vehicles, which cost the city $45,000 in repairs.

Mike DeBonis contributed to this report.