"By the end of the day, if the weather cooperates, we can probably get all of our tourists out of there," Blair said.
Helicopters had evacuated about 170 visitors and residents from Supai by Sunday night.
No damage was reported in the village, which is accessible only by trail and helicopter, but officials said some trees were uprooted and some downstream trails and footbridges were washed out.
There were no reports of injuries. Authorities on the ground and in the air were searching for about 11 campers and tourists who remained unaccounted for, though they may have left on their own, Blair said.
The situation was "certainly nowhere near as dangerous as it was yesterday," he said Monday.
Mimi Mills and 15 others were rescued Sunday morning after a flash flood washed away their rafts while they were on a hike the afternoon before. Mills was among about 35 evacuees who spent Sunday night at a shelter in Peach Springs, about 65 miles southwest of Supai.
"It was definitely frightening, and there was a lot of, 'Whoa, what are we going to do next and what's the morning going to bring?" Mills, 42, of Nevada City, Calif., told The Associated Press in a phone interview Monday.
She said the group took shelter overnight under an overhang, but had to scramble up a cliff when another flash flood occurred in the middle of the night.
"I woke up to people yelling, 'We've got to get out of here!"' she said. "We booked it up a cliff in 10 seconds, and we just saw this massive rush of water rage down the creek side."
Rescuers worked throughout Sunday to locate campers and Supai residents and evacuate them to the top of the canyon if they wished. Blair said tourists were not being allowed back into the canyon.
The canyon, on tribal land, is a less-traveled alternative to Grand Canyon National Park to the east. Visitors hike several miles down the canyon to reach a series of spectacular waterfalls.
The area of northern Arizona got 3 to 6 inches of rain Friday and Saturday and about 2 inches more on Sunday, said Daryl Onton, a National Weather Service meteorologist in Flagstaff. Early Monday, about 0.80 of an inch more fell on the area, the weather service said.
"That's all it took - just a few days of very heavy thunderstorms," Onton said.
About 6 a.m. Sunday, the Redlands Earthen Dam about 45 miles upstream from Supai was breached, park officials said. The small dam forms a pond to provide water for livestock. It isn't a "huge, significant" structure and its rupture was only one factor in the flooding, said Blair.
In 2001, flooding near Supai swept a 2-year-old boy and his parents to their deaths while they were hiking.
Associated Press Writer Mark Carlson contributed to this report.