Three other passengers and the pilot were injured.
The six passengers on board were visiting from the United Kingdom, Police Chief Francis E. Bradley Sr. of the Hualapai reservation said.
Passengers Becky Dobson, 27, Jason Hill, 32, and Stuart Hill, 30, suffered fatal injuries in the crash, according to a news release from the Hualapai Nation Police Department. Their bodies were recovered early Sunday afternoon.
The survivors of the crash were rescued during an operation that stretched into the early hours of Sunday morning, Bradley said.
The injured pilot was identified as Scott Booth, 42. The hospitalized passengers were identified as Ellie Milward, 29, Jonathan Udall, 32, and Jennifer Barham, 39, according to the police news release.
In a statement, Bradley expressed his condolences to the family and friends of the crash victims.
He said first responders and rescuers had arrived at the scene within 30 minutes of the crash: "Without their valiant and diligent efforts to stabilize and rescue the survivors under extreme conditions, we may have had more loss of life," he said.
Bradley earlier said first responders had been hindered by windy, dark and rugged conditions and had a 20-minute hike to the crash scene.
Rescuers got help from military aircraft from Nellis Air Force Base in Las Vegas and were eventually able to fly all four of the injured to the University Medical Center in Las Vegas, he said. The pilot had severe injury to one of his limbs.
Photos of the crash scene showed flames and dark smoke rising from rocky terrain.
Teddy Fujimoto told CNN affiliate KSNV he was in the area taking photographs when he witnessed the aftermath of the crash.
"I saw these two ladies run out of it, and then an explosion. One of the survivors ... looked all bloody. Her clothes probably were burnt off," Fujimoto told KSNV.
"The ladies were screaming. ... It was just horrible," he said.
FAA spokesman Allen Kenitzer earlier said the aircraft sustained considerable damage in the crash.
The FAA and the National Transportation Safety Board will investigate, Kenitzer said.
The company says it flies roughly 600,000 passengers a year on Grand Canyon and other tours. It also notes that it "abides by flight safety rules and regulations that substantially exceed the regulations required by the Federal Aviation Administration."
"It is with extreme sadness we extend our heartfelt sympathy to the families involved in this accident. Our top priority is the care and needs of our passengers and our staff," Papillon Group CEO Brenda Halvorson said Sunday.
NTSB investigators determined the probable cause of the 2001 crash was pilot error.
CNN's Marilia Brocchetto and Joe Sutton contributed to this report.