Hillary Clinton staked a claim to the southern black vote on Tuesday, receiving a warm welcome at one of the country’s most important black churches just a day after Donald Trump failed to win public approval from another group of black church leaders.

“This is the day that the Lord has made,” Clinton said at the start of her speech in Montgomery, Alabama, and by the second half of the sentence the congregation had joined in: “Let us rejoice and be glad in it.”

Elsewhere, Clinton has received criticism from new civil rights activists, like the leaders of the Black Lives Matter movement, who say she isn’t doing enough to address modern concerns. But her deft turn in Alabama showed the depth of Clintonian influence in an area where even other Democratic candidates have faltered. Her leading party challenger, Bernie Sanders, has struggled to win basic name recognition in the south.

Clinton spoke on the 60th anniversary of Rosa Parks’s bus protest in Montgomery, Alabama, which sparked the civil rights movement in America. Hundreds of people packed Dexter Avenue Baptist church – the church Martin Luther King Jr pastored – to hear Clinton speak. She delivered the keynote address at the gathering, which was convened by the National Bar Association, the country’s largest organization of black attorneys.

Hillary Clinton joins hands to sing We Shall Overcome after her speech at the Dexter Avenue King Memorial Baptist church. Photograph: Hal Yeager/AP

Mary Hunter, 75, dressed in her finest clothes, drove to the capital from Pike Road, Alabama, and stood in line for four hours to enter the church. She said she remembers hitching rides into Montgomery as a teenager during the bus boycotts, and 10 years later she marched into the city with King. She was determined to hear Clinton’s speech, she said, because a woman’s campaign for the presidency of the United States seemed like a civic bookend to Rosa Parks’s action 60 years earlier.

“Women have always played an important role. It’s just now coming to the fore,” she said.

Before Clinton spoke, 85-year-old Fred Gray stepped to the pulpit. He served as the attorney to Parks and King, and helped orchestrate the bus boycotts. He was on a mission, he said, “to find everything segregated and destroy it”.

Clinton then spoke about the evolution of civil rights in more recent years. “There is something profoundly wrong when African American men are far more likely to be stopped and searched by police, charged with crimes, and sentenced to longer prison terms for doing the same thing as a white man,” she said.

Mary Hunter stood up from her pew. “Amen,” she said.

Clinton said: “We must strengthen the bonds of trust between law enforcement and the communities they serve.” To accomplish that, she said, means “we must end the era of mass incarceration”.

She added: “We must do more to address the epidemic of gun violence that is plaguing our country.”

She offered few specific solutions, though, that might appease activists. Afterward, the president of the National Bar Association, Benjamin Crump, said such differences are a natural shift from one generation to the next. “I welcome Black Lives Matter,” he said. Crump worked on the seminal cases of Trayvon Martin and Michael Brown, both prominent instances of violent deaths of young, unarmed black men in recent years. “It’s just an evolution.”

Asked whether Clinton, as a presidential candidate, should call for a legal change requiring local police departments to report deaths during confrontations with police, Crump told the Guardian: “Absolutely. In this day, with all the technology we have, it’s ridiculous for them not to report that. Absolutely.”