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Tampa, Florida, police said Wednesday that they are confident a 24-year-old man taken into custody on Tuesday is the man wanted in a string of shooting deaths.

"Finally, this morning, we were able to say it was day one of the healing process," Police Chief Brian Dugan said Wednesday. "That's a good feeling for us. It's a happy day. But I can also tell you, it's the beginning of a lot of work."

Howell E. Donaldson III was taken into custody in Tampa's Ybor City on Tuesday after entering the McDonald's where he worked and asking a fellow employee to watch a bag for him, an affidavit said.

The co-worker approached an officer who happened to be in the restaurant and handed over a McDonald's food bag that contained a ".40 caliber Glock firearm loaded with SIG brand Smith and Wesson ammunition," police said. Donaldson was detained when he returned to the McDonald's.

Dugan said at a news conference that Donaldson admitted to owning the gun but didn't confess to the four murders and didn't turn himself in. It was the gun, Dugan said, that linked Donaldson to the four killings.

Tampa Mayor Bob Buckhorn said that although police are confident they have the right person, "I think it's important that the process take place."

"I think at the end of this, if he is found to be guilty, he should die. It's that simple," Buckhorn said, adding: "For 51 days, we had a neighborhood that was held hostage."

Related: Tampa killings: Suspect Howell Donaldson to be charged with murder

Dugan said police aren't sure what Donaldson's relationship is with the neighborhood of Seminole Heights, where all four murders took place. Donaldson told police he isn't familiar with the area and isn't associated with anyone there, according to a police report.

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Dugan said that Donaldson, who was cooperating with police, had been charged with four counts of first-degree murder but that evidence still needed to be collected and that there is a "tremendous" amount of work ahead.

"He was friendly and nice to the cops, but he didn't tell us why he was doing it," the police chief said, adding that no confession was given.

Delonda Walker, general manager of the McDonald's where Donaldson was detained, and J.C. Prado, the restaurant's operator, told NBC News that they were fully cooperating with police, to whom they referred all requests for comment.

"I am so proud of my wife for handling that the way that she did," Walker's husband, Mateen Walker, told NBC affiliate WFLA-TV. "She is a soldier and such a strong sister. I couldn't be any more proud of her than that."

Law enforcement agents investigate a fatal shooting in the Seminole Heights neighborhood in Tampa, Florida, on Nov. 14. Jones, Octavio / AP

It remained unknown whether Walker would get any of a total of $110,000 that had been offered in rewards for the killer's arrest, or if so, how much. But Richard Gonzmart, president of Columbia Restaurant in Ybor City, stopped by to give her a check for $9,000 on Wednesday.

"She doesn't look at herself as a hero," Gonzmart told WFLA. "How do you not look at yourself like a hero to take this monster off the streets? She's a hero in my eyes."

Dugan said a sense of relief hit him Wednesday morning knowing a suspect is in custody, but he added, "To have four unsolved homicides on your watch is a tough pill to swallow."

"I'll carry that with me for the rest of my life," he said.

Donaldson graduated in January from St. John's University in New York, where he was a non-scholarship player for the basketball team during the 2011-12 season, the college confirmed. Donaldson never appeared in a game, the school told NBC News.

D'Angelo Harrison, a teammate now playing professionally in Turkey, told The Torch, the St. John's student newspaper, that he and Donaldson often played on the recreational courts after practice. He called Donaldson a "hard-nosed defender," the newspaper reported.

"I couldn't believe it," Harrison said of Donaldson's arrest. "It's a sad thing."

The string of killings began Oct. 9, when Benjamin Mitchell, 22, was shot while he was waiting for a bus.

Related: Potential Fourth Murder Victim of Tampa Serial Killer Found

Four days later, Monica Hoffa, 32, was found dead in a vacant lot. The following week, Anthony Naiboa, 20, was killed while he was walking.

The body of Ronald Felton, 60, was found Nov. 14 near the scene of a memorial honoring the first three victims. His brother told NBC News that Felton, the father of three adult children, had been on his way to feed the homeless at a church when he was shot.

With the families of the victims gathered behind them, officials said they hoped this chapter in Tampa's history would be over and a new one could begin.

"We're good. Sun is shining," Buckhorn said. "Tampa is ready to move on. Turn the page."