The film and television actor Christian Oliver, his two children and a pilot were killed on Thursday when the small plane they were traveling in crashed during a flight to the Caribbean island of St. Lucia, the police said.

Mr. Oliver, 51, who appeared in “The Good German,” “Speed Racer” and the TV series “Saved by The Bell: The New Class,” and his daughters were the only passengers in the single engine plane traveling from Bequia, an island of St. Vincent and the Grenadines, when it crashed into the sea at midday, the Royal St. Vincent and the Grenadines Police Force said in a statement on Thursday.

In addition to Mr. Oliver and his daughters, Madita Klepser, 10, and Annik Klepser, 12, the pilot, Robert Sachs, was also killed, the police said. Fishermen and divers recovered the bodies and turned them over to the St. Vincent and the Grenadines Coast Guard, the police said in a statement on Friday.

The aircraft “experienced difficulties and plummeted into the ocean” shortly after taking off from J.F. Mitchell Airport in Bequia, the police said. There was no further information about the cause of the crash, which is under investigation, they said.

Mr. Oliver was born in Germany and had dual citizenship there and in the United States, his agent in Berlin, Caprice Crawford, said in an email on Friday. He used the name Christian Oliver in his professional work rather than his full name, Christian Oliver Klepser, and divided his time between Los Angeles and his home country, she said.

Mr. Oliver worked with Steven Soderbergh in the 2006 film “The Good German,” with a cast that included George Clooney and Cate Blanchett. His other projects included a role in “Valkyrie” with Tom Cruise in 2008 and “Indiana Jones and the Dial of Destiny,” in 2023, for which he provided voices.

He had just finished shooting a new movie, “Forever Hold Your Peace,” and posted a photograph from the set on social media about a week ago.

Earlier this week, Mr. Oliver posted his last photograph “from somewhere in paradise.”

Mr. Oliver was co-producing “Forever Hold Your Peace,” a story about marriage fraud, with the director Nick Lyon. Mr. Lyon said in an interview on Friday that Mr. Oliver had texted him on Thursday morning about his plan to return to the United States to work on a scene on Friday.

“It was a big project for us,” said Mr. Lyon, who had also worked with Mr. Oliver on “Hercules Reborn” in 2014. “We had talked about it for years.”