The suspect is a registered sex offender and has served prison time, the mayor said. In police interviews, the man led them to believe he might have been influenced by convicted serial killer Anthony Sowell, Norton told The Associated Press.
"He said some things that led us to believe that in some way, shape, or form, Sowell might be an influence," the mayor said.
Sowell was found guilty in 2011 of killing 11 women and hiding their remains around his Cleveland home from June 2007 to July 2009. Police found their mostly nude bodies throughout the house after a woman escaped and said she had been raped in there.
Sowell's victims ranged in age from 24 to 52, all were recovering or current drug addicts and most died of strangulation; some had been decapitated, and others were so badly decomposed that coroners couldn't say with certainty how they died.
Prosecutors described him in court papers as "the worst offender in the history of Cuyahoga County and arguably the State of Ohio." He was sentenced to death.
On Saturday, Police Commander Mike Cardilli announced that a woman's body had been found Friday in a garage and two other bodies were found a day later — one in a backyard and the other in the basement of a vacant house.
All three people are believed to have been killed in the last six to 10 days.
Police did not know the identities of the three victims. Norton said police believe the three were female, although the bodies had not yet been examined by the medical examiner.
Norton said the bodies were each in the fetal position, wrapped in several layers of trash bags. He said detectives continue to interview the suspect, who used his mother's address in Cleveland in registering as a sex offender, the mayor said.
Cardilli said the man was arrested after a standoff with police Friday. Police did not immediately release the suspect's name. He was jailed in East Cleveland, the mayor said.
"The person in custody, some of the things he said to investigators made us go back today," the mayor said.
Police searched vacant houses over about three blocks in the neighborhood Saturday and planned to expand their search Sunday, Norton said.
The police, FBI, the Ohio Bureau of Criminal Investigation and the Cuyahoga County Sheriff's Department went through yards and abandoned houses and used dogs trained to find cadavers.
The neighborhood in East Cleveland, which has some 17,000 residents, has many abandoned houses and authorities want to be thorough, the mayor said.
"Hopefully, we pray to God, this is it," he said.
The Cleveland area has had its share of gruesome news in recent years. In May, three women who separately vanished a decade ago were found captive in a run-down house. Ariel Castro, a former school bus driver, has been charged with nearly 1,000 counts of kidnap, rape and other crimes.
Castro is accused of repeatedly restraining the women, sometimes chaining them to a pole in a basement, to a bedroom heater or inside a van. The charges say one of the women tried to escape and he assaulted her with a vacuum cord around her neck. He also fathered a daughter with one captive, authorities said.
He has pleaded not guilty to all the charges.