Financier Jay Bloom shared text messages between himself and Rush where Rush dismissed concerns from Bloom and his son Sean about taking the trip on the Titan submersible.
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"While there's obviously a risk it's way safer than flying in a helicopter or even scuba diving," Rush texted.
One text revealed Rush offered Bloom and his son a "last minute" discounted price of $150,000 for each of them.
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"Filling up this year and next. Want to reserve a spot(s)?" another text said.
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Bloom and his son turned down the offer due to safety concerns.
Rush even flew to Las Vegas on a homebuilt, two-seater plane to try and convince them, Bloom said.
"He flew to Vegas on an experimental home-built plane to pitch me on going on an experimental home-built sub," Bloom told ABC News.
The vessel suffered a "catastrophic implosion" based on debris located 1,600 feet from the wreckage of the Titanic, the Coast Guard said Thursday. Rush and the other four passengers aboard the experimental deep-sea vessel "have sadly been lost," according to the submersible company.
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The tragedy is raising questions about OceanGate's sub design and operations.
"He drank his own Kool-Aid and he sort of had this predisposition that it was safe, and anybody who disagreed with him, he felt it was just a differing opinion," Bloom said. "He just kind of was going to go with what he believed."
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ABC News contributed to this report.