Since the beginning of 2014, three children have been shot in the city, and those cases remain unsolved.
"No child should grow up gathering memories of being shot in their neighborhood. That is unacceptable, and I am outraged," said Jones.
The mayor urged the community to "say something if you see something suspicious." Jones also said getting illegal guns off the streets is a top priority.
A 23-month-old girl is recovering from injures she suffered after she was shot inside her South Richmond apartment Sunday. Police sources said the shooting appeared to be accidental.
A five-year-old child was injured during a shooting at a Mother's Day cookout in Richmond's Whitcomb Court last month. No arrests have been announced in connection with that shooting.
“With all of those people present, no one has come forward to specifically identify a suspect and be willing to back that up with testimony and that troubles me,” Chief Tarasovic said after the shooting. “I am terribly concerned that we have not received an outcry from the community that cause us to make not an arrest, but an immediate arrest.”
The May 1 beating death of eight-year-old Marty Cobb made international headlines. The South Richmond child was beaten while defending his older sister from a teenage attacker, Cobb's family said. Police arrested the suspect in this case.
Chief Tarasovic pointed out that the crime rate is "only slightly higher" in 2014, but added that Tuesday's press conference was called because of the "recklessness" involved in the recent string of shootings. The chief called the recent spike in crime a community problem and asked for the public's help.
"If that community support starts to wane then it's my job. It's our job to restore that community trust of us," Tarasovic said.
When asked if citizens would be protected if they tipped off police, Tarasovic said that if a tip is given anonymously, it will remain anonymous.
"But the problem with anonymous information you can't get convictions on anonymous information," Tarasovic said.
Carrie Cox, a member of Southside Debaters Seeking Solution 4 Change, said she tipped off police and officers protected her.
Cox reiterated that police cannot do their job alone.
"They can pick up bullets off the ground and they can do all the forensics in the world," Cox said. "But to have people stand around and actually see this, and not say anything about that's a tragedy."
However, one Fulton Hills resident, who spoke with CBS 6 on the condition of anonymity, said city leaders could do one thing immediately that she thinks would help.
"We need more police officers. We need more resources," she said.
The woman said she worries about her own safety after the shooting outside a convenience store where a 7-year-old was caught in the crossfire in February.
"That little boy got hurt and nobody knows who done it -- and that's not fair. That's somebody's son," she said.
If you have information about any of these shootings that could help police, please call Crime Stoppers at 804-780-1000.