In addition to providing charter flights, Island Express operates helicopter flights to and from Catalina Island.
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The day after the crash, the company issued a statement, saying it is cooperating with the National Transportation Safety Board investigation.
"We are deeply saddened by this tragedy," the statement said. "Our top priority is providing assistance to the families of the passengers and the pilot. We hope that you will respect their privacy at this extremely difficult time."
The helicopter pilot, who was killed in the crash, Ara Zobayan, had been with the company more than 10 years and had more than 8,000 flight hours, the company said.
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The investigation into what caused Sunday's fatal crash is expected to take a year or more. The aircraft's condition, maintenance records and pilot experience all are expected to be examined as part of that investigation, as well as factors such as weather.
The company has offered tours of Catalina and Southern California since 1982, according to its online marketing materials.
The company did not offer further details as to why it was suspending its other flights or when they might resume.