Police say the suspect was armed with about 44 more rounds of shotgun ammunition when he was stopped. He fired as many as 15 rounds in the class.
"To the people who showed courage in the face of such violence, and intervened to prevent this tragedy from being any worse, we owe you a debt of gratitude," Bend Police Chief Mike Krantz said on Friday.
Police offered more information on the attack at at a news conference on Friday, where they identified two of the four victims. They include five-year-old Rhoam Summer and 25-year-old teacher Meghan Lambert.
The families of the two other students who were killed, an eight-year-old and 11-year-old, did not wish to have them publicly identified yet, police said.
Two others were injured in the attack. Another teacher, a 54-year-old, was still being treated at hospital, and a seven-year-old student, who was in serious but stable condition.
Krantz said the heroic actions of both the teacher and the father who ran inside the school saved lives.
He said the teacher who wrestled with the gunman was not hurt but "almost certainly helped prevent more bloodshed".
He identified the suspect as 16-year-old Griffin J. John II, who previously attended the school and was a special educational needs student there.
A search warrant has been executed at the suspect's home and a search is ongoing, the police chief said.
Police believe the suspect travelled to the elementary school on foot, but police are still investigating his exact movements and how he acquired the gun. A motive is also not clear.
Officials did not confirm the name of the father who intervened and fatally shot the suspect.
But Kaylub Giamanco's family has identified him to US media as the person who sprang into action.
The 36-year-old carpenter had just finished lunch and was on his way home when he passed the school, his brother told NBC News. He saw the suspect open fire on a vehicle outside the school then shoot through a window and go inside.
Police said he had a legally concealed .40 caliber in his vehicle and his brother said he grabbed the pistol "and decided to go in after" the suspect. Police say he fired at the suspect "multiple times", killing him.
In a statement to the BBC's partner CBS News, Giamanco's family said he is a "lifelong resident of Bend" and that he "is not seeking recognition".
The family said Giamanco wants to express his "gratitude to the first responders, school personnel, and community for the outpouring of love and support". He and his family "respectfully ask for privacy".
US President Donald Trump praised the bystander's actions on Friday, calling him a "great hero".
Addressing reporters at the White House before departing for Georgia, Trump said the situation could have been "much worse" with no intervention.
"It's a terrible thing, but thank goodness for a man that had a gun and knew how to use it," he said.
Without naming the bystander, Governor Kotek acknowledged the man's heroic actions stopping further loss of life, but noted they "carry a heavy emotional burden, and I just want you to know that my thoughts are with you as well".
Kayla Epstein contributed to this report.