The pleas come during another holiday weekend with at least 16 people already shot, and two of them killed.
Jones was inside her Austin neighborhood home on June 20 when a stray bullet came flying in.
Nearly three months after her death, police continue to search for her killer.
"I don't want anybody to join this club of losing a child; it's painful," said Lawanda Jones, Amaria's mother.
The youngest of five, Lawanda said Amaria wanted to be lawyer.
RELATED: Mourners remember girl, 13, killed by stray bullet on West Side during funeral
"She loved to talk, and she wanted to be heard," her mother said. "She wanted you to see her and hear her."
Amaria also liked to dance. She was showing her mother the latest routine on TikTok when she was killed.
"I heard a weird noise and something shattered in my face," Lawanda said. "I turned around and my baby was on the ground holding her neck, reaching out, saying 'mom.'"
Amaria was killed during a violent Father's Day weekend. A total of 78 people were shot and 11 were killed that weekend.
WATCH: 'Nothing has been done' since Amaria's murder, older sister says
"I don't want anybody else's family to endure what me and my family endured," said Mercedes Jones, who became emotional as she mourned her younger sister.
RELATED: Chicago shootings: Violent weekend comes amid push encouraging police to take part in 'blue flu'
Mekhi James, 3, was shot in a separate incident the same day in Austin.
"I just want my sister back. I want to tell her I miss her. I just want to grab her, hold her tight and kiss her," said Omarion James, her brother.
Jones' family gathered Saturday on Chicago's West Side hoping to stop further gun violence, especially attacks on children.
"All I'm asking for the government, the government, the mayor reach out, help," Mercedes Jones said. "This has to stop. This has to stop somewhere."
Joined by activist Rabbi Michael Ben Yosef, the group called on Gov. JB Pritzker to declare gun violence a public health crisis.
Demonstrators also asked for legislation in Amaria Jones' name and better support for the Austin community, including economic development.
"To bring about change, to bring about resources, to bring about protection for all these homes that deserve to live in peace, not to be dodging bullets," said Rabbi Michael Ben Yosef, Chicago Activist Coalition for Justice.
Mayor Lori Lightfoot said in a written statement Saturday evening: "Since day one of this administration, Mayor Lightfoot has been clear that the City needed to shift away from a law enforcement-first-and-only strategy, and focus on enhancing coordination with trauma-informed services, block clubs, streetoutreach and community-based organization as well as key City departments like public health, family and support services and schools. That's why in her first budget as mayor, she invested a monumental $11.5 million in community-based public safety as part of the City's 2020 budget, a seven-fold increase in funding compared to last year and the largest year-over-year increase in recent history. Just this past spring, we awarded $7.5 million of those funds to 10 community-based organizations from across 15 Chicago communities in an effort to expand street outreach and trauma-informed victim services for those who are at the highest risk of violence. On top of that, the City is investing an additional $10 million towards our violence prevention efforts through CARES Act funding.
"The violence we are facing each weekend is the result of decades of disinvestments in our South and West Side communities. And through monumental investments like these and unprecedented programs like INVEST South/West, we can continue to build on our all-hands-on-deck effort to address the root causes of violence and keep our neighborhoods safe. The City's budget is a moral document that reflects the values and priorities of our great city, that's why as we continue working on our financial plan for 2021, we are focused on building on the successes of last year's investments and ensuring it reflects the needs of our residents."
ABC7 Chicago has reached out to Gov. JB Pritzker's office, but has not heard back.