"When I hear the words 'police violence', personally, I suffocate," Macron's new Interior Minister Gérald Darmanin said in the French National Assembly.
His phrasing has drawn further criticism at a time when many questioned his appointment after he faced an investigation over a rape allegation.
"The police use violence indeed, but in a legitimate way. [...] It needs to be proportionate and subject to a framework. When it is executed outside of the rules, they should be immediately sanctioned," he added.
Darmanin's sparked anger due to his use of the word "suffocate", echoing the words of a delivery driver who died after being pinned to the ground by French police.
Cédric Chouviat, 42, died on January 5 of asphyxia and a broken larynx. He repeated "I'm suffocating" nine times while on the ground.
In a statement, lawyers for Chouviat's family said they were "shocked" and "offended" by Darmanin's comments.
One of the lawyers tweeted saying: "Mr Darmanin, you have just ignored the limits of decency."
The issue of police violence has been a hot topic over the past few years in France due to events like the death of 24-year-old Adama Traoré to police's handling of the yellow vest protests.
The hashtag #DarmaninResign (#DarmaninDemission) was on French Twitter on Wednesday.