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Minot, North Dakota (CNN) -- Minot and other North Dakota cities dealing with record flooding will continue to be threatened by the Souris River for days to come, even though the water is no longer rising along parts of the river, a U.S. Army Corps of Engineers commander said Monday.

Although the river crested in Minot early Sunday morning, it has only dropped a fraction of an inch since -- leaving crews with the tense, around-the-clock job of constantly inspecting and shoring up emergency levees built to protect critical structures, said Lt. Col. Kendall Bergmann, deputy district engineer for the Corps' St. Paul District.

"We're 99% complete, but it's an ongoing fight," Bergmann said Monday.

The river had crested in Minot and appeared to be cresting in the downstream community of Velva, Bergmann said. The remaining communities along the U.S. portion of the river -- which begins in Canada and loops back into that country downstream of Minot -- do not appear threatened, he said.

Overnight, crews had to deal with floodwaters seeping through storm sewer drains and levees, but none of those issues posed major threats, he said.

Workers had to build another ring levee near the Broadway Bridge to protect that critical north-south route through Minot from being cut off, Bergmann said. National Guard helicopters also had to drop one-ton sandbags around a school to keep it from flooding.

The Souris River crested Sunday at Minot at nearly 13 feet over flood stage -- below earlier predictions, but still almost 4 feet above an 1881 record, according to the National Weather Service. The river had fallen about 6 inches as of Monday morning, according to the weather service, and is predicted to remain above the 1881 record into next week.

The state was scheduled to open three recovery centers in North Dakota on Monday -- two in Minot and one in Bismarck -- for residents in the throes of the record-setting floods.

Residents can visit the locations to find out about assistance programs and have their questions answered, Gov. Jack Dalrymple told reporters. But, he said, it is not necessary for residents to visit the centers to register for disaster assistance, which can be done by telephone or online.

Dalrymple said a tour of the area Sunday was "sobering, to say the least."

A boil-water order, issued as a precaution Saturday, remained in effect. Minot officials told residents that tap water should be boiled for at least a minute before consuming in order to kill any dangerous organisms.

Republican Rep. Rick Berg said he had been in touch with officials in Washington -- which has authorized FEMA to grant assistance -- and expressed optimism that the government will work well with residents to overcome the challenges.

"You're seeing people at the highest levels working together, putting politics behind them," said North Dakota's lone congressman.

Many residents of Minot who evacuated ahead of the rising water returned to the area Sunday against the recommendations of the city officials, hoping to catch a glimpse of their homes, said CNN's Jim Spellman.

Spellman said when he toured the hardest-hit area by boat, several residents gave him their addresses and asked him to check on their homes. Everyone was hoping his or her home might be the one that was spared, he said, but he had to bring back bad news.

"It's a somber feeling, sitting here," said resident Steve Knab. He recalled "listening to the sirens go off, and they evacuated us, and coming back the next day and seeing this ... it's disheartening."

But, he said, "We'll get there. We're healthy."

Evacuee Robin Taylor said residents have been helping one another. When her family had to evacuate in a hurry, neighbors on both sides pitched in, she said.

Jim Sarroll has lived in Minot his entire life. He has sandbagged his home, located just outside the evacuation zone, with the help of neighbors, and said Sunday it was dry so far.

He was, however, very concerned about the water. "I flushed my toilet this morning, and the water was red," he said.

Still, he said he was able to see the positives, when neighbors, relatives and friends bond to get through a disaster the best they can.

CNN's Ed Payne, Alexandra Steele, Mike Pearson, Holly Yan, Phil Gast and Sara Weisfeldt contributed to this report.