What It Means: Fears of increased crime override calls for police reform.

Republicans had rallied around the measure as a means of reducing crime in the state, listing instances where a minor traffic infraction had led officers to uncovering drug trafficking and violent crimes.

“It’s time to take handcuffs off police and put them on criminals where they belong,” said State Senator Brent Taylor, a Memphis Republican.

But Democrats warned that the Republican supermajority was undoing a key reform. “It’s a slap in the face,” said State Senator London Lamar, a Memphis Democrat, adding that the ordinance did not impede efforts to stop reckless driving or violence in the city.

Republicans, however, denied that the bill would cause additional harm.

Behind the Tensions: A running fight between the legislature and Tennessee’s biggest cities.

The Republicans in control of state government have repeatedly taken aim at the autonomy of Tennessee’s largest, and largely Democratic-led, cities.

In the last couple years, the legislature has sought to exert its authority over Nashville and Memphis, whose leaders are increasingly at odds with the Republican proposals in the legislature. Nashville, in particular, has battled legislation that would shrink the size of its council and overtake the board of its airport authority.

“We have to do everything in our power to protect local control when it comes to matters of life and death of our community,” State Representative Justin J. Pearson, a Memphis Democrat, told reporters on Thursday.

Tyre Nichols’s family: ‘We worked too hard to get this passed.’

Mr. Nichols’s mother, RowVaughn Wells, and his stepfather, Rodney Wells, drove from Memphis to the State Capitol in Nashville repeatedly this month, pleading with lawmakers to allow the law to remain in place.

“Coming back to Nashville is the easy part because we want to see justice done,” Mr. Wells said on Thursday. “We worked too hard to get this passed.”

But the pair, after speaking with Mr. Taylor, the lead Senate sponsor, left before it was debated. Mr. Taylor confirmed that he declined their request to delay debate and passage, adding afterward that he “thought it best to go ahead and have closure for the family and also the community back home.”