On Thursdays, the Daily News reported that Tim McShea, vice president of the International Association of Fire Fighters Local 22, said he also received a notice of another shortage at 9:30 p.m. Tuesday.
Not true, Sawyer said Thursday. The city's ambulance corps did not tap out at that time.
But McShea says the city runs out of available medic units "almost every day, especially during the summer on a hot day."
Whoever is right, Sawyer insists "we are working to make the system better. This is not the first time we've heard about this issue."
The commissioner said the Fire Department is set to spend $2.4 million to hire 80 EMTs, who will be divided into separate classes of 40 trainees.
Sawyer said he expects them to be ready for action later this year, following a seven- to 10-week training course.
The city will implement a new plan that calls for one EMT and one paramedic to respond to advanced life-support calls, instead of the current approach, which calls for two paramedics.
The department will also spend another $6 million between now and the next fiscal year to replace 25 ambulances in the city's aging fleet, Sawyer said.
McShea said earlier this week that in the best of circumstances, 9-1-1 callers face a five- to seven-minute wait for an ambulance, if they're lucky - but also sometimes have to wait upward of 30 to 45 minutes.
"Our average response time is eight minutes and 15 seconds, which is within the national standard," he said.
When asked if residents ever have to wait a half-hour or more for an ambulance to arrive, Sawyer said, "That's an anomaly, something that happens once in a blue moon. That's not the average by any means."
The commissioner said the Fire Department has rented extra medical units to cover the city for the typically busy Fourth of July holiday weekend, and paramedics are also working overtime to help handle the likely influx of extra calls.
"I understand the union's position, but it's not fair for them to give information out without providing the right numbers," he said. "We're doing what we can to improve things."
But City Controller Alan Butkovitz, whose office produced audits in 2007 and 2011 that lambasted the Fire Department for slow emergency response times and other organizational problems, said he was "outraged" when he learned that the city twice ran out of medics this week.
"It's the same old, same old," he said. "The city's poor response time is scandalous. . . . They should not be giving you an anecdote that everything's OK."
On Twitter: @dgambacorta