The fire started Friday morning north of Neola, about 100 miles east of Salt Lake City, and on Sunday morning crews had it about 5 percent contained. The cause had not been determined.
The fire began spreading into the Ashley National Forest Sunday afternoon, prompting federal authorities to close it to public use.
The small communities of Whiterocks, Farm Creek, Paradise and Tridell were evacuated Saturday. Some residents in Tridell had been allowed to return.
The Federal Emergency Management Agency said about 300 people are under a mandatory evacuation. Another 150 homes in Dryfork Canyon, about 8 miles northeast of the fire, could be threatened by Tuesday, said Derek Jensen, a FEMA spokesman.
"We are seeing extreme fire behavior and the potential for growth is still there. We haven't had a change in weather or change in fuel type or dryness," said Louis Haynes, a spokesman for the national forest.
At nearby Vernal, there was little wind Sunday, the temperatures hit 95 degrees and midday humidity was only 10 percent, according to the National Weather Service.
Edson Gardner, of Fort Duchesne, went to Farm Creek to evacuate his mother, whose home was burned to the ground.
"It came down the canyon like a herd of horses," he said Saturday. "The sheriff told us we had five minutes to get out."
Uintah County Sheriff Jeff Merrell said buildings had been destroyed but he didn't have a count.
A U.S. Forest Service command team that travels the country fighting the largest fires joined local crews Sunday and took over direction of the firefighting efforts.
Eleven-year-old Duane Houston escaped the fire but his father, 43-year-old Tracy Houston, and his grandfather, 63-year-old George Houston, were killed by the flames Friday as they worked in a hay field, authorities said. The owner of the field, 75-year-old Roger Roberson, died at a hospital, officials said Saturday.
The Houstons had gone to buy hay from Roberson, and were helping him move irrigation sprayers on his field in an attempt to block the flames.
Duane said he was told to run for their truck as flames and smoke filled the air.
"I ran and couldn't find the truck, so I kept running through trees, climbed two fences and followed the road," he told The Salt Lake Tribune. He was treated at a hospital and released.
Utah Gov. Jon Huntsman's request for aid from FEMA was granted on Sunday. A federal grant will pay 75 percent of the state's eligible firefighting costs.
In Montana, fire managers on Sunday were reducing personnel assigned to a blaze that had burned nearly 6 square miles in the Gallatin National Forest. Evacuation orders remained in effect Sunday for several dozen summer homes, the Madison Arm Resort, some campgrounds and a ranger station.
In California, crews battled a wildfire Sunday that had blackened more than 700 acres of brush in a rugged area of Santa Barbara County near popular campsites and swimming holes.
That fire, which started Saturday evening, was 50 percent contained Sunday morning, U.S. Forest Service spokesman Robert Rainwater said. The blaze had closed some campgrounds, but no residents had been ordered to leave their homes, he said. The cause of the fire was under investigation.
Fire crews north of Los Angeles had a 19-square-mile blaze 90 percent contained, state fire department spokesman Shawn Sternick said. Twelve houses and six other buildings had been destroyed since the fire broke out a week ago in steep canyons south of the San Joaquin Valley, officials said.