At least three people were killed and 50 others were injured after an Amtrak train derailed in Montana on Saturday afternoon, setting off a frantic response by rescuers who scrambled to extricate passengers from cars, the authorities said.

Amtrak said that eight cars on an Empire Builder train had derailed at about 4 p.m. local time near Joplin, Mont., which is about 200 miles north of Helena. About 141 passengers and 16 crew members were on board, “with injuries reported,” Amtrak said in a statement.

The train consisted of two locomotives and 10 cars, and the tracks are run by BNSF Railway.

“Amtrak is working with the local authorities to transport injured passengers, and safely evacuate all other passengers,” the passenger rail service said in a statement.

The Liberty County Sheriff’s Office said that three people were confirmed dead.

Amanda Frickel, the disaster and emergency services coordinator for Hill County, Mont., said in an interview that “well over” 50 people had been injured. The train was heading west when it derailed, she said.

She said that rescuers from six counties were responding to the scene and that as many as five hospitals were on standby to receive injured passengers. There were also a number of medical helicopters standing by, she said.

“Everybody who is alive has been extricated from the wreck,” Ms. Frickel said.

Officials had evacuated survivors to two separate sites and were doing a head count. Emergency responders planned to put people up in hotels once their medical needs had been seen to.

“Every county around is assisting,” said Sheriff Donna Whitt of Toole County, Mont.

The National Transportation Safety Board said on Twitter that it was launching a “go-team” to investigate the derailment.

Megan Vandervest, who was going to visit a friend in Seattle, boarded the train on Friday night from Minneapolis, where she lives.

On Saturday afternoon, she was asleep in the first car when she was jolted awake.

“My first thought was that we were derailing because, to be honest, I have anxiety and I had heard stories about trains derailing,” Ms. Vandervest said. “My second thought was that’s crazy. We wouldn’t be derailing. Like, that doesn’t happen.”

She soon figured it out. The car she was in was fully on the tracks.

But the car behind hers was tilted over, the one behind that was entirely tipped over, and the three cars behind that “had completely fallen off the tracks and were detached from the train,” she said.

Speaking from the Liberty County Senior Center, where passengers were being taken, Ms. Vandervest said she felt lucky that she and the three other people she was with were not injured.

In her car, she said, it felt like “extreme turbulence on a plane.”

Austin Knudsen, Montana’s attorney general, said that Montana Highway Patrol troopers were among those helping with the rescue efforts. “We are praying for the safety of all passengers and crew who were on board,” he said.

Karen Jelly, who works at Holland and Bonine Funeral Home, in Havre, Mont., said the funeral home was waiting for a dreaded phone call from the authorities. “It’s going to be very bad when we get that phone call,” she said.

Ms. Jelly, who moved to Havre nine years ago from Wyoming, said the area is extremely welcoming.

She said the community “rallies around people when things go bad.” Now, she said, “it’s going to be marred by this memory.”

While derailments of Amtrak trains are rare, there have been deadly crashes in recent years.

In 2018, three people died after an Amtrak train traveled on the wrong track in South Carolina and slammed into a parked freight train. That same year, a train carrying Republican members of Congress hit a garbage truck in rural Virginia, killing a passenger in the truck.

In 2015, an Amtrak train that had been traveling at more than 100 miles per hour, twice the speed limit, careened off a curve in Philadelphia, killing eight people and injuring more than 200.

Andrés R. Martínezand Austin Ramzycontributed reporting.