WASHINGTON — President Obama engaged in a verbal tussle with the Texas lieutenant governor, defended Black Lives Matter and held an impromptu meeting with the daughter of a Staten Island man killed by police as he spent another day grappling with racial tension roiling the U.S.

A town hall-style discussion Obama taped with ABC News’s David Muir on Thursday at a theater in Washington was disrupted at its conclusion by Erica Garner, the daughter of Eric Garner, who was killed by police. Erica Garner was upset that she didn’t have a chance to question the president at the hourlong forum.

President Obama greets audience members after participating in a town hall discussion taped with ABC news anchor David Muir in Washington Thursday. Associated Press/Carolyn Kaster

It was the third day in a row that Obama addressed tensions between minority communities and law enforcement in the U.S., following shootings by police last week that left black men dead in Louisiana and Minnesota and a rampage by a gunman in Dallas who killed five cops policing an otherwise peaceful protest against police brutality.

Before Garner’s outburst, the town hall was marked by a heated exchange between Obama and Texas Lt. Gov. Dan Patrick, a Republican who has made controversial remarks after police-involved shootings, including the Dallas attack.

“This isn’t a matter of us versus them,” Obama testily told Patrick, who had asked the president whether he was doing everything he could to protect police. “This is a matter of all of us Americans working together.”

After the Dallas shooting, in an interview with Fox News, Patrick mocked protesters who fled the scene as “hypocrites” and blamed members of the Black Lives Matter movement for inciting the violence.

Obama, in response to a question from Edward Flynn, the white Milwaukee police chief, issued a full-throated defense of the Black Lives Matter movement and its name, saying it serves to bring attention to inequities in poor and minority communities. Flynn has lashed out at Black Lives Matter activists, accusing them of focusing on police brutality to the exclusion of high murder and crime rates in Milwaukee’s black neighborhoods.

The name of the movement, Obama said, is “not meant to suggest that other lives don’t matter; it just means that other folks aren’t experiencing this particular vulnerability. We shouldn’t get too caught up in this notion that people who are asking for fair treatment are somehow automatically anti-police or are trying to only look out for black lives compared with others.”

After the Dallas attack, Obama abbreviated a trip to Europe and flew to the Texas city on Tuesday to speak at a memorial service for the slain officers. On Wednesday, he convened an hours-long meeting at the White House with police officials, minority community activists and academics to discuss the violence and heightened tensions. He attended Thursday’s town hall event at the invitation of ABC, which chose the participants.

Obama said Thursday that he feels compelled to speak when he thinks adding his voice to the conversation can help calm the country.

“If I don’t say anything at a time when people feel hurt and angry and protests flare up, then I wouldn’t be doing my job,” he told a white college sophomore at the ABC event who asked why he views tensions between police and minority communities through a racial lens.

Another young man asked Obama whether he’d ever been pulled over by police and how he was treated.

Obama said he’d been speeding and deserved to be pulled over most of the times that it had happened, but he recalled a hurtful episode when he was 10, living in Hawaii with his white grandparents. As he boarded an elevator to his grandparents’ apartment, he said, an older white woman who lived on their floor stepped off and declined to ride with him.

Peering through the peephole of the apartment, he watched her come up after him and realized “she just didn’t want to go up with me,” he said.

“There’s a greater presumption of dangerousness that arises from the social-cultural perceptions that have been fed to folks for a long time,” Obama said. “I think it’s not as bad as it used to be, but it’s still there. That presumption can also lead to really dangerous situations.”

At the event’s conclusion, Erica Garner yelled profanities at network officials and demanded to meet with Obama. He obliged, meeting privately with the woman whose father was killed on Staten Island two years ago this week after he was put into a choke hold by police investigating whether he was illegally selling cigarettes.

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