Sen. Bernie Sanders (I-Vt.), a Democratic presidential candidate. (Win McNamee/Getty Images)

A day after being heckled by Black Lives Matter protesters at a progressive conference in Phoenix, presidential hopeful Bernie Sanders spoke out against police brutality at a pair of large-scale rallies Sunday in Texas.

“We want a nation where a young black man or woman can walk down the street without worrying about being falsely arrested, beaten or killed,” Sanders, the independent senator from Vermont, said during a stop in Dallas that reportedly drew 8,000 people to a hotel ballroom.

Later Sunday, during an evening rally in Houston, Sanders brought up the case of Sandra Bland, a 28-year-old African American woman found dead in her jail cell 60 miles northwest of the city after being arrested for a traffic stop. Her family has disputed a medical examiner’s finding that the death was a suicide.

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Sanders also cited other recent deaths of African Americans in encounters with police in New York, Baltimore and Cleveland.

“These are the cases that you have heard about recently, but anyone who thinks this has not been going on decade after decade would be very wrong,” Sanders said, addressing a crowd of more than 5,000 in a Houston arena. “It is unacceptable that police officers beat up people or kill people. If they do that, they have got to be held accountable.”

His comments came a day after protesters interrupted back-to-back appearances by Sanders and former Maryland governor Martin O’Malley at the Netroots Nation conference in Phoenix, an annual nationwide gathering of progressive activists.

The protesters demanded that both Democratic presidential hopefuls detail how they would address police brutality and other issues affecting African Americans. Many of those who rushed the stage were affiliated with the group Black Lives Matter, which was formed after the shooting death of teenager Trayvon Martin in Florida.

Sanders appeared visibly irritated by the disruption of his “town hall” appearance Saturday, saying at one point, “If you don’t want me to be here, that’s okay.”

Sanders spokesman Michael Briggs said the senator wanted to include a section on police brutality in his remarks while in Texas because of the proximity of the Bland case. It is not clear, he said, whether Sanders will continue to include those remarks in his stump speech, which focuses largely on economic issues.

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Sanders, who continues to draw large crowds on the campaign trail, has surged in polls in Iowa and New Hampshire, emerging as the leading challenger to Hillary Rodham Clinton for the Democratic nomination. His audiences, however, have been largely white, and he has acknowledged his campaign needs to do a better job reaching out to African Americans and Latinos, two key constituencies in the Democratic nominating process.

Sanders’s rallies in Texas were among several planned in coming weeks in Southern states with sizable African American populations. Aides says the senator also plans to travel to Mississippi, Alabama, Georgia and South Carolina.

Speaking in Washington, D.C. Thursday, Democratic presidential candidate Bernie Sanders said the shooting deaths of nine people in an African American church in Charleston, S.C. show "the ugly stain of racism that still taunts and taints our nation." (Bernie Sanders)