Ron Thomas met with Mayor Richard Jones for two hours in the morning, ending with both sides saying they had a better understanding of each other.
"He's deeply concerned about my son and he absolutely wants to know the truth of what happened and how my son died," Thomas said.
Despite a warm meeting Wednesday, Thomas urged Jones to resign for what he calls a lack of leadership.
"I told him I wasn't. There's a job that still needs to be done," Jones said. "I'm just upset myself about what has happened to this wonderful city. This one issue cannot destroy a city of 135,000."
The meeting was unlike what Thomas had to say to Jones at the Fullerton City Council meeting Tuesday as frustrations continue to build over the July confrontation in which Kelly Thomas, 37, was severely beaten by six officers.
"Mr. Mayor, I came here tonight to offer you an olive branch, but the first thing you do is open your mouth and I want to grab a baseball bat instead, I swear to God," Thomas told the mayor Tuesday night.
Thomas has backtracked about that inflammatory comment, admitting he had no intention of bringing a baseball bat to the one-on-one meeting with the mayor.
One thing he's not backing down from is his call for Jones and others in city government step down.
"I'm not going to stop until he does [step down], and last night, he just wouldn't shut his mouth. Everything out of it was so bad, so derogatory, so insensitive, that I'd had enough by that point," Thomas said.
Tuesday's meeting also drew furious remarks from community members.
At one point, some council members walked out of the meeting because tensions were running so high. However, all members returned to the meeting and they decided to hire an independent attorney to investigate Thomas' death.
On July 5, officers responded to a report of a man breaking into cars at the Fullerton Bus Depot. They struggled with Kelly Thomas after trying to search his backpack. He was hospitalized with severe head and neck injuries and was taken off life support and died several days later.
Family members, who said Thomas was schizophrenic, say police used excessive force.
Investigations are under way by the Fullerton Police Department, the FBI and the Orange County District Attorney's Office in addition to the new independent investigation launched by the Fullerton City Council.
The attorney hired by the council, Michael Gennaco, promised the concerns of the community will be addressed.
"Every case is different and every community is different, but I have been struck in this case from my perspective at how this incident has seemed to have struck a nerve with members of that community," Gennaco said.
The six officers who are involved in the incident are on paid administrative leave and Fullerton Police Chief Michael Sellers has taken an indefinite medical leave. Capt. Kevin Hamilton was appointed acting chief in the interim.