At a news conference in Beverly Hills, Trump appeared alongside several activists who have lost family members in crimes or traffic accidents involving immigrants in the country illegally.
"People came into the country illegally and killed their children," Trump said. "The illegals come in and the illegals kill their children."
Trump made the comments the day before he was scheduled to appear at a campaign rally in Phoenix with controversial Maricopa County Sheriff
"It's this issue," he said. "I must be doing something right."
In the weeks since he called Mexican immigrants "rapists" and criminals in his campaign announcement speech, Trump has risen in the polls, with several now showing him among the top GOP candidates. But the backlash has also been fierce, with several major companies, including NBC Universal and Macy's, cutting ties with Trump for fear of losing Latino customers.
Immigrant advocates in Los Angeles made their distaste for Trump clear with a large protest outside another event. Trump spoke to Friends of Abe, a group founded a decade ago by several conservative-leaning Hollywood actors, including Gary Sinise and Clint Eastwood.
About 150 protesters gathered outside the event, some toting "Dump Donald Trump" signs and others taking whacks at piñatas created in the business mogul's image.
Joshua Gonzalez, a 21-year-old Calabasas resident holding a sign depicting Trump in a pink wig, said he came to send a message that Californians won't put up with "his out-of-control antics."
Gonzalez said Trump was hurting the Republican Party, which might otherwise appeal to conservative Latinos who believe in the importance of education and hard work.
"Donald Trump creates division among the races in California and across the nation," Gonzalez said. "He is trying to exploit divisions."
Several dozen Trump supporters also gathered outside the event, many wearing red, white and blue and carrying signs reading, "Trump Tells the Truth."
Things got heated, with protest organizers and a security officer trying to keep the sides apart as one man jabbed his "Trump for President" sign at protesters while a woman yelled back, "Racist!"
At the news conference with victim-advocates, Trump acknowledged that he has become a firebrand, saying the head of the Republican National Committee called him recently and asked him to "tone it down."
"I don't want to tone down important issues," Trump said. "I'm so proud of myself for bringing this issue to bear, to the forefront."
Trump appeared alongside the family of Jamiel Shaw Jr., an L.A. high school football star who was killed in 2008 by an immigrant in the country illegally, and other victim advocates.
In recent days, Trump has focused his criticism on San Francisco's sanctuary policies, under which a Mexican immigrant in the country illegally was released from custody and subsequently charged with murder in a high-profile shooting July 1.
On Friday, Trump repeated his claim that Mexico is sending "criminals" to the United States and pledged again to build a wall along the southern U.S. border to keep them out.
He seemed unfazed by accusations from some that he is promoting xenophobia, at one point predicting he would win the Latino vote.
"When it's all said and done, I will win the Hispanic vote," Trump said. "I will win the Hispanic vote because I'm going to create jobs. I'm going to take them away from China."
His rhetoric would spell political suicide if he were running for office in California, where the Republican loss of statewide power is often attributed to the party's hard line on illegal immigration. Attempts to push through statewide ballot measures ending public benefits for those without legal status and welfare payments for their children have failed.
But beyond California, Trump's words appeal to a significant slice of the national Republican base, allowing him to distinguish himself among 16 candidates vying to win the party's presidential nomination, one analyst said.
"There is a highly bigoted group of people who use the GOP as a venue to achieve political power and influence, and Trump is appealing to that element," said Allan Hoffenblum, a Republican consultant and chief author of the California Target Book.
Trump's attacks on Latino immigrants have won him widespread media coverage — he was mentioned on one national cable news network more than 240 times in a 24-hour-period, Hoffenblum said. "It's been effective," he said of Trump's rhetoric. "He won't be nominated, but what will be interesting is to see how far he goes."
Trump has put many Republicans in a difficult spot.
Along with Flake, Arizona's senior senator, Republican John McCain, and Gov. Doug Ducey will not attend Trump's Phoenix rally.
Still, some leaders of the Arizona GOP said they were ready to welcome Trump.
"In Maricopa County we believe deeply in Reagan's 11th commandment that 'Thou shall not speak ill of any other Republican,'" the party said in a statement. "It is disappointing when our Republican leaders do not share that same commitment to party unity and teamwork."