Passenger Heidi Rendalen told Norwegian broadcaster NRK she heard several bangs and saw lights flashing after the plane took off.
"It was banging four, five times at the same time as there were lights flashing and I heard behind me: it is burning, it is burning," she said. "I thought I was done for."
"I believe there was a fire in the engine. I'm not sure but they are saying the engine didn't work," she added.
Rendalen said people were panicking and screaming in the back of the plane. "The only thing I could do was to look at my partner and the children and hold their hands," she said.
The plane was in the air about 10 minutes, AENA spokeswoman Karen Martel told The Associated Press from the island.
Martel denied that one of the plane's engines had caught fire, saying only it had undisclosed trouble.
Iberworld said in a statement the plane had suffered "a technical problem" in one of its engines. It gave no details.
The company said the plane was carrying 180 passengers. It did not say how many crew, but a company official said an A320 normally carries a crew of six.
The passengers were taken off the plane and the company planned to put them on a different one bound for Oslo, Martel said.
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