Ward 19 alderwoman Alfreda Edwards did not know his name, but she would wave to him, recognizing him by his gray clothes and hat, as he went in and out of the halfway house across the street from where she lives. But on Thursday, his body was found on their street, rolled up in plastic inside a trash can.

“It’s just so traumatizing,” Edwards said.

As an alderwoman, she said she is not sure what she can do about the city’s recent spate of murders — three of which occurred between Thursday and Saturday, including the one that affected Edwards. But she and other city officials said Monday that they need to work with the community to fight gun violence. At a press conference Monday, Mayor John DeStefano Jr. said the city will also try to find ways for parents to feel comfortable notifying authorities about criminal behavior without the risk of having their child arrested and with school officials so that the city can identify students who might be prone to violence. The city also wants to “redouble efforts” to help ex-felons assimilate back into normal city life, DeStefano added.

The press conference Monday marked the first time city leaders have spoken publicly to discuss the crime wave, responding to the continuing violence and rising anxiety in the city. New Haven Police Department Chief Frank Limon, who was sworn in just last week, said he will work on strategies for his “Operation Corridor” policing campaign, which was just launched this weekend and increased police presence in the area where the recent murders occurred. But Limon declined to comment on what new strategies he would use, adding that he prefers to work “behind the scenes.”

In response, Jeffie Frazier, formerly a principal at the Wexler/Grant Community School, said at the press conference that she hopes that the chief will work with community leaders — herself included — to fight crime.

Since the end of last year, there have been 17 homicides, 15 of which involved firearms, Limon said. Most of the victims were in their late 20s or 30s and were recently released from prison. All were black.

The assailants, Assistant Police Chief Stephanie Redding said after the press conference, were either in their late teens and 20s. Although some victims were affiliated with gangs, Limon said, only two of the recent murders were directly related to gang activity. City and police officials explained that the majority of the murders are the results of personal fights.

“Individuals are using firearms to settle personal conflicts,” Limon said.

Police responded to multiple gunshots on Saturday that were fired in the Dixwell neighborhood around 4:15 a.m. and found New Haven resident Kenneth Thomas, 29, who was shot at 43 Charles St. Limon said Monday that investigators have learned since the shooting that there were witnesses in the area who did not alert police.

“We need the community to report crime,” he said.

But Claudine Wilkins-Chambers, who lives around the corner from Edwards, said community members are fearful that if they report a crime, the assailant will come back and retaliate.

In response to the gun violence, black community leaders staged a rally in Dixwell on Sunday to ask state troopers to patrol the city’s streets. DeStefano said at the press conference Monday that the city would rather work with the state authorities to encourage people to come forward and report crimes.

“They have got real fears that the people they are informing live just down the street, and they’ve got to deal with this,” he said. “We’re not there with them every hour of every day to protect them, and that’s a real concern.”

Edwards said she may open up the Celentano Museum Academy, at 400 Canner St., for after-school programs. Ward 22 Alderman Greg Morehead said he organized a community meeting Thursday that he hopes will build trust between residents and police.

City Hall spokeswoman Jessica Mayorga said the city is also planning to hold a public meeting with the mayor and community leaders on Thursday night.