Venezuela's state TV has shown a video of a US citizen apparently confessing to plotting to overthrow President Nicolás Maduro and bring him to the US.
Luke Denman is one of 13 people arrested over the weekend. Venezuela says they are "mercenaries" whose armed incursion was foiled.
Mr Maduro has often accused US President Donald Trump of trying to invade the country and overthrow him.
Mr Trump earlier this week denied any US involvement.
Secretary of State Mike Pompeo has said the US government will use "every tool" to secure the return of the Americans.
What did Venezuelan TV broadcast?
In Wednesday's video, Mr Denman, 34, appeared to explain that he was hired to train Venezuelans in Colombia before returning to Caracas and taking control of an airport to allow Mr Maduro to be taken out of the country.
"I was helping Venezuelans take back control of their country," Mr Denman, a former special operations forces member, is seen as saying.
Mr Denman said he and Airan Berry, 41, were contracted by Jordan Goudreau, an American military veteran who leads a Florida-based Silvercorp USA firm, to carry out the operation.
Venezuela said it would seek extradition of Mr Goudreau, who has admitted he was involved in the operation.
According to Mr Maduro, Silvercorp signed a contract with opposition leader Juan Guaidó, a politician seen by the US and many European countries as Venezuela's legitimate leader.
"Donald Trump is the direct chief of this invasion," Mr Maduro said during a press conference, after the video of Mr Denman was broadcast.
The Venezuelan president said the Americans would have a fair trial.
He did not provide any information as to the whereabouts of the detained men. It is unclear if they have access to a lawyer.
Who are the detained US citizens?
Not much is yet known about Mr Denman and Mr Berry.
Venezuelan military high command have said the pair are members of the US security forces. US media have suggested they are former members - but this has not been confirmed.
Caracas says that 11 other people were arrested, and eight armed men killed during the alleged coup attempt.
What is the background to this?
Mr Goudreau has also repeatedly made claims about past associations with Mr Guaidó.
On Monday, Mr Guaidó denied having anything to do with the ex-Green Beret. In a statement, he said he had "no relationship nor responsibility for any actions" taken by the US war veteran.
He also accused President Maduro's administration of trying to distract people from recent outbreaks of violence - including a deadly prison riot on Friday and a gang battle in Caracas on Saturday night.
What do we know about Jordan Goudreau?
The Canadian-born US military veteran heads the US company at the centre of the plot to overthrow the Venezuelan president.
A former Green Beret who received a number of bravery awards, he served 15 years in the US Army, first in the infantry as a mortar specialist, and later as a special forces medical sergeant, the Washington Post newspaper reports.
He was deployed to Iraq and Afghanistan twice between 2006 and 2014, army officials quoted by the Post say.
In 2018, he set up Silvercorp USA, a private security firm, in Florida.
The firm advertises a variety of services, including assisting victims of kidnapping and extortion. It claims to have "led international security teams" for the president of the US.
Silvercorp's website advertises operations in more than 50 countries, with an advisory team made up of "former diplomats, former heads of security for multinational corporations, and the most experienced and viable military, law enforcement and intelligence professionals in the industry today", without naming them.