A recent string of operational problems and misconduct allegations has embroiled the D.C. fire department and prompted concerns that a dysfunctional agency is undermining public safety.

The department’s troubles run the gamut: a labor-management spat over a visit by firefighters to the White House, charges of sexual harassment at the training academy, and the death by heart attack of a man who waited 29 minutes for an ambulance on a day when more than 100 firefighters called in sick.

In the background are long-standing tensions between managers and the local firefighters union over the direction of the department. The relationship hasn’t been helped by discord over management proposals that would deal with such concerns as longer emergency response times and a shortage of paramedics, in part, by concentrating more shifts during peak times of the day.

Fire Chief Kenneth B. Ellerbe has said the changes are necessary because more than 80 percent of the calls are for medical emergencies, not fires. Union leaders say that the chief has failed to hire paramedics fast enough to keep pace with attrition and that his mismanagement is forcing D.C. residents and visitors to wait longer for less­-than-adequate care.

The new chairman of the D.C. Council’s public safety committee, Tommy Wells (D-Ward 6), is taking a cautious approach. He said he has just begun to delve into a complex array of issues clouded by animosity between the union and the chief that renders virtually every detail subject to debate. During sworn testimony last month, Ellerbe and the union president, Edward C. Smith, could not even agree on how many paramedics left the department last year. Smith said 20; the chief said 12.

Wells, who is contemplating a run for mayor, said he is focusing on issues with the greatest effect on the public. He has asked the D.C. inspector general to investigate the allegations of sexual harassment at the training academy and the circumstances under which fire engine mechanics earned as much as $97,000 in overtime in the past fiscal year.

Ellerbe, testifying at a public safety committee hearing last month, said the overtime payments were made to 10 mechanics because managers allowed too many of their co-workers to take leave at the same time. He promised new protocols to keep it from happening again. “We weren’t paying as much attention to it as we are now,” he said.

The chief said he reacted quickly to sexual harassment allegations in which two female recruits said an instructor’s inappropriate remarks made them feel uncomfortable.

At the hearing, Ellerbe tried to win support for his plan to change the way firefighters’ working hours are scheduled. Firefighters now work a single 24-hour shift followed by three days off. He wants them to work shorter but more frequent shifts. He has also proposed taking advanced-life-support paramedics off the street from 1 to 7 a.m. to free up resources for later in the day. Union leaders are vehemently opposed to altering shift times, arguing that changes would disrupt the lives of 1,800 members.

In his testimony to the committee, Ellerbe acknowledged that the department has difficulty keeping its paramedic ranks filled, and he described efforts to recruit military veterans with medical backgrounds.

About response times, Ellerbe said that in 84 percent of cases, a firetruck or ambulance reaches a high-priority patient in less than 61 / 2 minutes, with the average being 41 / 2 minutes. But during the day, Ellerbe said, when demand is highest, “the number of ambulances available is reaching the limit of our department’s service capacity.”

The chief said in 88 percent of high-priority daytime calls, ambulances reach patients in 12 minutes or less, with the average being 71 / 2 minutes. The chief said it can take as long as 15 minutes for ambulances to reach patients in some neighborhoods. Paramedics or emergency medical technicians aboard firetrucks often arrive and provide treatment first.

Union representatives, speaking at the same hearing, blamed the chief. “This is a manufactured crisis,” Joe Papariello, who chairs the emergency medical systems committee of D.C. Firefighters Association Local 36. “We are seeing an exodus of paramedics, and nothing is being done about it.”

Slow response times were especially evident at the end of last year. A week after firefighters were excluded from a Christmas bonus given to thousands of other workers, an unusual number of them called in sick New Year’s Eve. The city says 106 firefighters, paramedics and emergency medical technicians — about one-third of those scheduled to work— didn’t show up on one of the busiest weekends of the year.

The city blamed the union, and the union denied that there had been an organized sickout. But no one has denied that the situation led to a mad scramble to staff fire engines and ambulances, cost a considerable amount in overtime and delayed urgent care. One man died of a heart attack after waiting 29 minutes for help. Fire officials said no fire engine or ambulance was available anywhere in the District for 16 minutes after the first 911 call came in.

Ellerbe has denied that delays contributed to the man’s death, a contention that the family has disputed.

The labor-management dispute has even tarnished feel-good moments. On Feb. 19, firefighters from across the region stood with President Obama in the White House as he discussed the effect of budget sequestration. Prince George’s County officials sent a congratulatory message over Twitter. But the D.C. fire chief scolded his firefighters, complaining that their appearance had not been cleared through his office or the mayor’s office.

In a statement, Ellerbe denied that anyone had been disciplined over the White House visit, but he asked for written reports so that protocols could be set for future invitations. That rebuke sent a chill through the ranks, said Smith, the firefighters union president, who, in protest, boycotted a mayoral luncheon held to praise city employees for their hard work during Obama’s inauguration.

“It’s the city’s way of continuing to disenfranchise the firefighters,” Smith said. “When you read between the lines, it boils down to control.”