They shared photos of water rushing over riverbanks and encircling homes and neighborhoods.

Floodwaters had surrounded the town of Fremont, Neb., about 40 miles northwest of Omaha, said Councilwoman Linda McClain. The town sits between the Platte River to the south and the Elkhorn River to the north. Both rivers had overflowed their banks, Ms. McClain said.

“We’re like an island,” she said. “You cannot get in or out.”

Ms. McClain said she spent Saturday visiting shelters where people who had been displaced were congregating. About 75 people had been reluctant to leave their homes, but as the buildings took on water, they were rescued by airboats and taken to the shelters, she said. Many homes were flooded by as much as three or four feet of water.

Parts of the city had been under a mandatory evacuation.

“Right now, we’re in crisis mode,” she said.

Tech. Sgt. Rachelle Blake, of the United States Air Force, said several buildings on the Offutt Air Force Base, which is south of Omaha, had been evacuated as water from Papillion Creek, a tributary of the Missouri River, flooded the southeast part of the base. She said the northwest part of the base was largely unaffected.

She said that it was too soon to quantify the damage, but that buildings and hangars were underwater. Aircraft had previously been moved to higher ground.