The deep sea explorer said he raised his "significant concerns" about OceanGate's operations and the design and safety of its sub, but that Harding "decided to roll the dice" anyway.
"I told him he shouldn't get in that damn sub," he told the newspaper.
Vescovo, who founded expedition company Caladan Oceanic, said Harding was "set on" going to see the Titanic wreck.
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He claimed Harding asked him to go in his two-man submersible called Limiting Factor, but he turned down his offer.
He said: "I talked to Hamish about it and I told him he shouldn't get in that damn sub ... it was only a matter of time before they [OceanGate] kill somebody. But Hamish really, really wanted to go to the Titanic and that was the only opportunity ... now it's 'damn, why didn't I raise more fuss, should I have been more aggressive?'"
Vescovo tweeted on Friday: "This has been a difficult week for the submersible community. Deep ocean diving is very safe when industry standard certifications and procedures are followed. I will miss my good friends PH Nargeolet, who I worked with closely, and Hamish Harding, my friend in sea and space."
The day before the Titan set off on its fatal journey, Harding said in an Instagram post he was "proud" to be part of the expedition.
He said the trip was "likely to be the first and only manned mission to the Titanic in 2023" due to "the worst winter in Newfoundland in 40 years."
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