Houston Fire Chief Terry Garrison has stated that the administration's plan to cut transport ambulances and reduce on-duty staff will put the public at risk.
And Mayor Parker admits if the strictest form of her plan is put into action, it could affect HFD response times.
"There is no doubt that if we had to park a significant number of fire apparatus, it could have an impact on public safety."
But Parker says the goal is to avoid that by reorganizing how HFD is staffed and reducing what she calls excessive overtime in the department.
"We have done nothing, to date, that should compromise public safety. We have put staff positions back out into the field, we did a shake-up and reduction is the size of the fire command staff, we did a reduction in the size of the finance staff and took over the finance staff because they were having obviously difficulty managing the increased budget that they were given."
About a dozen Houston firefighters were present during the mayor's remarks, but declined to comment.
The firefighters' union is suing the city over its plan to bench some units.
Meanwhile, the city and the union are in contract negotiations over future pay and benefits for firefighters.