Police said that five boys were involved in the chase on Monday afternoon, and four went into the river.
The Maylands Boat Ramp on Clarkson Road was blocked off for police and emergency service access only, and just after midnight, police recovered the body of one of the teenage boys.
"My condolences and the condolences of all police to the families of the two deceased boys and the friends", WA Police Commissioner Chris Dawson told reporters Tuesday.
Police revealed overnight that the body of one teenage boy had been recovered from the water on Monday night.
"Police did not physically come into contact with the two boys who disappeared under water in the middle of the river".
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"This again is nothing short of a tragedy that has taken two young boys' lives", he said.
Some of them entered the river in a bid to escape and several were arrested, but it was unclear if there were more who did not make it out of the water.
They were part of a group being chased by police on Monday afternoon, and the incident will be treated as deaths in custody.
"Police responded at the scene and were able to safely recover two boys from the river".
The group of youths were allegedly jumping fences in Maylands yesterday.
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"Two boys are believed to have gotten into difficulties in the middle of the river and succumbed to the conditions, and were not seen to resurface".
"Our immediate concern is the welfare of particularly the fifth boy who we've been unable to locate and of course the ongoing welfare for the remaining four families and loved ones".
He was last seen, on foot, on the Swan River foreshore.
An extensive land and water search is continuing, involving SES volunteers, water police, mounted police and the airwing.
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