In a video shown on state TV, Luke Denman claimed he signed a contract with a Florida-based security company to train rebel troops and carry out an assault to remove Nicolas Maduro from power in exchange for up to $100,000.
He said the mission had been to secure an airport and then "bring in planes" including "one to put Maduro on and take him back to the United States", Sky News reported.
Denman and Airan Berry, both former Special Forces soldiers who served in Iraq, were arrested on Monday following what authorities described as a botched beach landing in the fishing village of Chuao.
Both men are associated with Silvercorp USA, a private firm founded by Jordan Goudreau, an ex-Green Beret, who said Operation Gideon was aimed at "liberating Venezuela".
In a virtual press conference, Maduro said the failed plot was coordinated by Washington, adding, "Donald Trump is the direct chief of this invasion."
Trump has said the US had nothing to do with the attack and that Goudreau is under federal investigation for arms trafficking.
Meanwhile, US Secretary of State Mike Pompeo said, "If we'd have been involved, it would have gone differently."
The operation, on Sunday, was allegedly financed by US-backed Venezuelan opposition leader Juan Guaido, according to Goudreau.
Guaido has denied the claim.
Eight people were killed at a beach near the port city of La Guaira - near the capital Caracas - during the foiled operation.
Eight others - including Denman and Berry - were arrested.
Footage said to show people detained after the raid was posted on Twitter and broadcast on state television.
The US has imposed tough economic sanctions against Venezuela in an effort to oust Mr. Maduro, who is accused of rigging elections in 2018.