Heavy rains on Saturday afternoon caused flash floods near the Cold Spring Swimming Hole, putting 14 family members in danger.
At least two of the dead were children, said Hornung.
She posted a video to social media showing the powerful water.
This grainy image taken from video of the floods shows a father clinging to a tree with his baby in his hand.
KNXV said dozens of people had been swimming in the river when the flooding occurred and quoted Medical District Fire chief Ron Sattelmaier as saying there was no way of knowing how many people were actually present.
"The clouds over on the other side of the mountain can be dumping buckets, and all of a sudden there's a wall of water coming through that just wipes out everything in its path", said Stevens, who has lived in the area for 20 years.
Sheriff J. Adam Shepherd said in the statement that a search-and-rescue operation was underway involving sheriff's deputies and the Arizona Department of Public Safety Ranger Helicopter, as well as members of the local Whispering Pines Fire Department and US Forest Service.More news: Russian Federation demands immediate return of diplomatic property from US
Disa Alexander was hiking to the swimming area when the water from Ellison Creek and East Verde River converged.
"They had no warning. In addition to the state of Arizona providing full air support, we will continue to assist in all ways possible", Ducey said.
"Deepest prayers for those lost in the Gila County tragedy, for their families and the entire community", Ducey tweeted. But he also said that despite previous flash floods in the region, it remained a popular destination.
A thunderstorm upstream rushed down from an area recently cleared by wildfires and in no time had flooded the area families were spending the afternoon, authorities said.
"We were on this trail, and 10 minutes into the trail, we started seeing water flooding down, just a lot of water coming down", said Mandisa Alexander.
The "burn scar" was one of the reasons the weather service issued the flash-flood warning.
An intense thunderstorm sent water, mud, and debris rushing down a mountain into the river below flooding the narrow canyon.