Sidonie Nargeolet said her 77-year-old father had been near the Titanic wreck 30 times, the first in 1987.
Rush, who is married to Wendy Rush, is chief executive of US-based OceanGate Expeditions which operates the Titan submersible.
OceanGate believes that the passengers on the Titan submersible have "sadly been lost" in a statement cited by CNN.
60-year-old Arthur Liobl described his trip aboard the Titan as a "suicide mission."
The issue was that OceanGate did not go through the industry's recognized certification process for the sub's design, fabrication and testing.
467336 (2002 LT38) is, if rounding up a bit, twice the size of the infamous sunken passenger liner, the Titanic, according to NASA. But we're in no danger of it hitting the Earth.
Five passengers were on the missing submersible that can keep them alive underwater for a maximum of 96 hours.
A five-person submersible vessel taking tourists on a $250,000 trip to see the wreckage of the 1912 Titanic disaster 12,500 feet (3,800m) undersea is missing in the Atlantic off Canada.
A submersible vessel taking tourists on a deep ocean journey to view the wreckage of the Titanic has been missing since Sunday. One pilot and four passengers are aboard.
US and Canadian ships and planes began swarming the area on Monday about 900 miles (1,450 km) east of Cape Cod, some dropping sonar buoys that can monitor to a depth of 13,000 feet.
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