At a morning news conference at City Hall, the mayor said she was sensitive to the plight of people in the inner city — if not from her own experience, then from that of her family.

“There’s a lot of pain in our city, and when you are in a position like mine, a lot of the frustration is, you know, fairly or unfairly, directed at you,” she said. “My parents grew up in Baltimore; I grew up in Baltimore. I’ve had cousins in jail, on drugs, killed; my brother was almost killed. I have cousins that are extremely successful, and I have family that are unemployed. We run the gamut, and I understand the problems. I can’t fault anyone for not understanding what’s on my heart.”

Ms. Rawlings-Blake grew up around politics and civil rights. Her father, Howard Rawlings, who was known as Pete, was a civil rights activist who became the first black man to become chairman of the powerful appropriations committee in Maryland’s House of Delegates. When she was a little girl, friends say, Ms. Rawlings-Blake would race through the corridors of the State House in Annapolis, telling her parents she wished they could live in the capital city full time.

With her father’s help, Ms. Rawlings-Blake became, at 25, the youngest City Council member in Baltimore history. Eventually, she rose to become the council president. In 2010, when her predecessor, Sheila Dixon, was forced to resign amid scandal, she stepped in as mayor. She won election in her own right the next year, and is up for re-election in 2016.

Ms. Dixon — hugely popular among black residents — is dropping hints about running against her.

At Mr. Gray’s funeral on Monday, when Ms. Rawlings-Blake was introduced, there was polite clapping. But when Ms. Dixon was introduced, the congregation roared with enthusiasm. “We love you, Sheila,” a woman shouted from the balcony.