A mother and her baby were shot doing something everyone should be able to do: enjoy time at a park with family, Seattle Councilmember Teresa Mosqueda said while the two remained in intensive care. 

The shooting that occurred at Pritchard Beach in Rainier Valley around 7 p.m. on Monday "underscores the deep need to move forward" on gun violence prevention programs and restrictions on firearms, Mosqueda said. Gun violence is "truly a public health issue," she added. 

Her comments came less than 24 hours after police say a 27-year-old woman and her 10-month-old child were shot while sitting in the back seat of a parked vehicle. As of Tuesday morning, the two remained in serious condition at Harborview Medical Center. 

Witnesses told police the victims were shot when at least two people opened fire on one another in a parking lot on Memorial Day. 

RELATED: Mom and baby in intensive care after South Seattle shooting

During the council briefing Tuesday morning, Councilmember M. Lorena Gonzalez said it "appears" two people began to argue in the parking lot and then began shooting at one another. 

"We take gun violence seriously without regard to who the victim is," she said. "But it becomes particularly concerning when children as young as two fall victim to gun violence." 

She was told police will continue to conduct emphasis patrols to deter such incidents. Ultimately, however, she said more common-sense gun legislation is needed to get firearms off the street. 

Seattle Mayor Jenny Durkan addressed the Memorial Day violence after a community walk in Capitol Hill.

"Make no mistake, this violence in unacceptable," she said. "We will investigate, we will hold people accountable, and we will make sure people can feel safe in their communities."

Deputy Chief Marc Garth Green was also there. He said it appears to be 'gang-involved,' but not necessarily strictly gang-related.

"The difference, in a lot of gang-involved shootings, members involved in the shooting are gang members," he said. "We don't know if it was a gang beef or if somebody disrespected somebody's sister, somebody else that caused the commotion."

Garth Green said he spoke to the victims' families at Harborview Medical Center on Monday night.

Police have not yet released suspect names or descriptions. Garth Green said police are working with ATF in an effort to link shell casings to other recent shootings.

At the same time, youth advocate Willard Jimerson Jr. called for more resources to be devoted to reaching youth.

"If we don't dig into them and give them internal value, the external value has no meaning," he said.

He believes programs like GROOM (Gifted Regardless of Oppressive Methods) of the Urban League of Seattle have a better chance of nipping violence in the bud — before police intervention.

"I want the public to know and understand – there is a reason for police involvement, police presence," he said. "A reason for politicians, senators – all different types of people that play a part in society. But there's also a reason for people who do this particular kind of work. And it's just as integral and needs to be supported as any of the different aspects we consider to be important."

Durkan echoed that message.

"The number one thing we can do ahead of this is be proactive about providing those strategies on community engagement," she said. "And making sure communities are the first front line, to make sure there are ways to resolve conflict other than through violence, and provide opportunity for youth at a young age."