ABC News reported Jeffrey Paul Cutlip, 63, called police in Brownsville, Texas, Saturday to say he had killed three or four people in Portland between 1970 and 1993.
Portland homicide detectives arrested Cutlip Sunday in connection with two homicides that took place in the city in 1975 and 1977.
The names of the victims had not been released.
"The next step is seeing what he says and seeing what they [detectives] can come up with," Brownsville police officer Billy Killebrew told ABC News. "He said he had been involved in three or four murders between 1970 and 1993."
Cutlip has convictions for first-degree sodomy and first-degree burglary, and he targeted women he didn't know "using threats and weapons to gain compliance," records show. He is listed as a "predator" on Oregon's sex offender database and Killebrew said he was arrested in Brownsville in April for failure to register as a sex offender, ABC said.
The (Portland) Oregonian reported Multnomah County Circuit Court records showed a warrant was issued Monday for Cutlip's arrest on the two counts of murder.
The newspaper said Cutlip was in the Cameron County (Texas) Jail awaiting extradition to Portland.