The Cessna 180 was destroyed by the impact and fire, Federal Aviation Administration spokesman Ian Gregor told The Associated Press.
"It was engulfed in flames on the ground," Alaska State Trooper spokeswoman Megan Peters said.
The second plane, a Cessna single-engine, sustained significant damage but was able to return to Anchorage International Airport and make an emergency landing after the collision near Trapper Creek, 80 miles north of Anchorage.
Pilot Kevin Earp, 56, of Eagle River was alone in the aircraft and uninjured, Peters said in a news release.
She said late Saturday that four bodies were recovered from the wreckage. Authorities initially said at least two people were killed.
The State Medical Examiner's office was working to identify the dead.
There was no immediate word on how the collision occurred.
It followed another collision between two planes earlier this month but nine people aboard the Piper Navajo and four people in a Cessna 206 floatplane survived uninjured.
The planes in the July 10 collision sustained some minor damage but were able to land safely in Anchorage, with FAA spokesman Mike Fergus then describing the incident as "almost unheard of."