Protesters with the Black Lives Matter movement argue with police to let them walk down the sidewalk during a rally outside Graceland on Elvis Presley Blvd Tuesday in Memphis, Tenn. (Mike Brown/AP)

Hours after he branded himself the “law and order” candidate for president, Donald Trump weighed in on another politically loaded term — one he proudly rejected: “Black Lives Matter.”

“A lot of people feel that it is inherently racist,” the presumptive Republican nominee told the Associated Press on Monday. “It’s a very divisive term, because all lives matter. It’s a very, very divisive term.”

Trump, who has a habit of starting a debate because “a lot of people” want him to, was not wrong about the phrase’s divisiveness. In the wake of last week’s police shootings of black men in Minnesota and Louisiana, and especially after the killing of five police officers in Dallas, fresh conservative thinking about race and crime has been stymied by those three words.

“I believe I saved a lot more black lives than Black Lives Matter,” Rudolph Giuliani, the former mayor of New York and one of Trump’s most reliable advocates in the Republican Party, said over the weekend. “I don’t see what Black Lives Matter is doing for blacks other than isolating them. All it cares about is the police shooting of blacks. It doesn’t care about the 90 percent of blacks that are killed by other blacks.”

Giuliani and Trump, who have sought and sometimes received the support of police unions, are among the most prominent people to argue that “Black Lives Matter” is simply too heated and accusatory to represent a serious call for reform.

The phrase Black Lives Matter first received national attention in summer 2014 and, since then, has become part of conversations on race in America. Here's how the phrase became a movement. (Claritza Jimenez,Julio Negron/The Washington Post)

Sen. Patrick J. Toomey (R-Pa.), who is up for reelection this year, has proposed legislation to expand consideration of the death penalty for criminals who target police, and he has bemoaned pushers of “this narrative” that “the police are systemically a bunch of racist rogues.”

The statement by the Dallas police chief that the shooter was aiming to “kill white people” has only strengthened critics’ objections to the phrase. Over the weekend, four plainclothes police officers walked away from their security jobs at a WNBA game when members of the Lynx, a Minneapolis-based team, wore “Black Lives Matter” shirts; on Tuesday, when the Lynx arrived in San Antonio, the shirts were notably absent.

[At Dallas memorial service, Obama aims to comfort nation after violent week]

To members and supporters of the Black Lives Matter movement, anger at the phrase is at best ill-considered and at worst malicious. The clear intent of the words, they say, is to emphasize that black lives matter as much as others.

They’ve scoffed as critics suggest the use of a slogan like “All Lives Matter,” as the radio host Glenn Beck did at an August 2015 rally “to end discrimination” that featured gospel music and a prayer from Rafael Cruz, the father of Sen. Ted Cruz (R-Tex.).

DeRay Mckesson, a prominent activist arrested in Baton Rouge over the weekend, accused Giuliani of “deflecting so that we are not engaged in a conversation about the abuses the police inflict on communities of color time and time again” in a Monday interview with MSNBC.

Polling has revealed a steady partisan divide in opinions of the Black Lives Matter movement. In a Pew poll released last month, just 20 percent of Republicans supported the movement, vs. 42 percent of independents and 64 percent of Democrats. Last September, a PBS News Hour-Marist poll found 17 percent of Republicans saying they agree with the movement; among Democrats, it was 51 percent. Those numbers largely track with the proportions of Republicans and Democrats who believe that racism is an institutional problem.

Protesters with the Black Lives Matter movement block traffic on Elvis Presley Blvd at the start of a rally outside Graceland on Elvis Presley Blvd Tuesday afternoon, July 12, 2016 in Memphis, Tenn. (Mike Brown/AP)

Some of the conservatives who wince at the term still say they want a fresh discussion of criminal justice reform. This year’s Republican Party platform, approved Tuesday in Cleveland, includes language about the need for prison reform. Sen. Bill Cassidy (R-La.), who has been in close contact with Baton Rouge constituents, said he was inspired by the healing language he’d heard from white and black people; it was just the term that rankled.

“I heard someone say it should be ‘Black Lives Matter, Too,’ as opposed to, ‘We matter, no one else does,’ ” he said. “There is an understanding that it’s about all people.”

Discomfort with the term has existed for the life of the movement, even from conservatives who think the activists have laudable goals.

“I think they should change their name, maybe — if they were ‘All Lives Matter’ or ‘Innocent Lives Matter,’ ” Sen. Rand Paul (R-Ky.) said during an appearance on Sean Hannity’s Fox News show last year. “I am about justice, and frankly I think a lot of poor people in our country, and many African Americans, are trapped in this war on drugs, and I want to change it. But commandeering the microphone and bullying people and pushing people out of the way I think really isn’t a way to get their message across.”

[Detective demoted after calling Black Lives Matter protesters ‘terrorists’]

Shamed Dogan, a black Republican state representative from Missouri, has worked with Democrats to introduce criminal justice reform bills. In the wake of last week’s shootings, he promoted them in a column for National Review, beseeching conservatives not to “condemn Black Lives Matter and President Obama” before they got to work.

“To heal America’s racial wounds, ease the escalating tensions, and end the violence, conservatives must lead the way on reforms that are both pro-black and pro-law enforcement, and do not entail curbing Second Amendment rights,” he wrote.

Chuck DeVore, a former Republican legislator who’s now a leader in the Right on Crime movement for conservative criminal justice reform, said the aims of Black Lives Matter do not overlap with what he and his allies are focused on. Soon, he said, Right on Crime scholars intend to collect data on whether nonwhite citizens are disproportionately affected by laws that led police officers to collect tickets for petty offenses.

In the meantime, the Black Lives Matter movement and its name remain problematic for Republicans, whether or not they favor reform. Dogan said Black Lives Matter activists have not made the inroads they need to in order to win legislative votes. He blamed much of that on tone.

“I don’t see anything wrong with either statement, ‘All Lives Matter’ or ‘Black Lives Matter,’ ” he said. “But I can see where some demands are just antagonistic instead of wanting reform. When people see those guys blocking traffic, it shuts them off, at least for people on my side. And they haven’t done grass-roots politics — it’s all this outside agitation.”