Eighty percent of the island is uninhabited. Most of it is a state park, and visitors aboard tour helicopters from several companies are a daily occurrence, weather permitting, the Coast Guard said.
The Waimea Canyon is among several attractions that draw tours there, the agency said.
Derek Kawakami, mayor of the County of Kauai, said Friday afternoon that "we ask for your continued thoughts and prayers."
The cause of the crash has not been determined, but it is the third helicopter crash in Hawaii this year, NBC affiliate KHNL of Honolulu reported.
U.S. Rep. Ed Case, a Democrat who represents a district in Hawaii that includes Honolulu, said in a statement Friday that more must be done to regulate the tour and small-aircraft industries and improve safety.
In September, Case introduced a bill he said would impose strict regulations on commercial tour operators, including helicopters and small planes. It would require that tour flight pilots focus on flying the aircraft and not also act as tour guides. It also would restrict where they can fly and how low.
"Tour helicopter and small aircraft operations are not safe, and innocent lives are paying the price," Case said in a statement Friday.
The FAA said it conducts random and regular surveillance on all Hawaii air tour operators and ensures companies address any issues. Ian Gregor, a spokesman for the Federal Aviation Administration, told The Associated Press the agency does not have concerns about the industry statewide.