The three other passengers in the helicopter were killed in the crash on Saturday. Allen Kenitzer, of the Federal Aviation Authority's Office of Communications, told AFP the aircraft sustained "substantial damage".
Late Sunday, a spokeswoman for the British Foreign Office told Sky News the government was "providing support to the families of six British visitors involved in a helicopter accident at the Grand Canyon on February 10, and we are in close contact with the U.S. emergency services".
Papillion Group, the company that organised the flight, released a statement promising full cooperation with crash investigators, and offered condolences to the victims and their families.
"It is with extreme sadness we extend our heartfelt sympathy to the families involved in this accident", Brenda Halvorsan wrote.
Strong winds, darkness and hard terrain hindered the rescue of those injured, with the casualties taken to hospital by helicopter after 9 p.m. local time, CNN reported.
Las Vegas-based photographer Teddy Fujimoto was photographing a wedding about 500 feet above where the crash occurred.
Authorities say the four were level 1 trauma patients.
Several incidents involving Papillon Airways, also known as Papillon Grand Canyon Helicopters, have been investigated in the past two decades.
"We are in the recovery and investigation mode now", Bradley said.
Officials from the National Transportation Safety Board were sent to the crash scene to begin investigating what caused the the Eurocopter EC130 helicopter to go down, Bradley said. That is about 60 miles west of Peach Springs, near the Grand Canyon's West Rim.
Earlier on Saturday, the National Weather Service had warned that conditions over the Grand Canyon were windy. According to the company's website, it flies about 600,000 passengers a year in its provided tours. The pilot and five passengers - who were all from NY - died.