The four people who died were shot and the victims were targeted, he said.
Police have been searching for the shooting suspects.
"Police have determined four people are deceased at three locations within a 5 km (3.1 mile) radius", the statement said. The man's decision to turn himself in was unusual, the officer said.
"For Penticton ... it's unprecedented", De Jager said.
They are asking the public to follow the direction of police and to avoid areas bordered by Eckhardt Avenue and Lakeshore Drive, and Main and Power streets.
"I understand that this is a deeply troubling incident that has taken place in our community", De Jager told a news conference.
All the victims appear to have known each other.
"The fact that we had the Emergency Response Team already en route, it was something that we made a decision to deploy them at that in the circumstances and information we had at that point", De Jager said.
Joyce Brennan, a downtown resident, said she was taking out the recycling sometime between 9:30 and 10 a.m. when she heard the sound of three muffled bangs in the distance.
She said her son called a short time later to say someone was killed near her house.
With a population of about 30,000, Penticton is a city in British Columbia in the country.
"We continue to ask that you remain inside and avoid the area".
She said she believed the shooting was the result of a dispute between neighbours, but her account has not been confirmed by authorities.
Three or four officers with rifles and a police dog charged down a nearby side street, while other police officers stayed behind and taped off the area, Halvorson said.
"I can say from an investigative perspective, we are glad he did that so the community isn't on pins and needles [worrying that he is at large]". "It's a very quiet area, so it's a little alarming for this to be happening".
About 45 minutes later, he heard a sound of "anguish", and his wife looked out the window and saw an older woman hugging someone, Kenward added. I just know she was upset.