A Miami-based security contractor who hired Colombian mercenaries accused of killing Haitian President Jovenel Moïse last month said he was working with a former Haitian Supreme Court judge to help arrest Mr. Moïse and not assassinate him.

Antonio Intriago, owner of a South Florida-based firm called CTU Security, said the mercenaries went to the president’s private villa to accompany Haitian police executing an arrest warrant for the president, according to a statement released Wednesday by three lawyers representing Mr. Intriago. They said the president was dead when the Colombians arrived, echoing testimony from some of the soldiers.

“It is our belief that the president’s own bodyguards betrayed him,” the lawyers wrote in a statement. It didn’t elaborate on why the bodyguards may have betrayed him.

The lawyers’ statement was accompanied by nearly 40 pages of private correspondence, contracts, a “Memorandum of Understanding” to replace Mr. Moïse with an obscure preacher, and an arrest warrant for the president. Together, the documents could shed more light on what happened in the early hours of July 7, when Haiti’s president was gunned down in the last few months of his term. The Biden administration has sent investigators from the Federal Bureau of Investigation and Department of Homeland Security to help Haiti solve the case; officials from Colombia have also offered assistance.

More than 40 people including members of the slain president’s security detail, Haitian politicians, a convicted drug dealer turned Drug Enforcement Administration informant, a second longtime DEA informant and Miami-area businessmen have been detained or implicated in the case.

The lawyers’ statement said the initial mission for the Colombian gunmen was to provide security for solar-power stations and other projects in the southern Haitian town of Jacmel. The statement said Mr. Intriago was approached by Christian Sanon, a little known Haitian-American preacher, who at some point informed Mr. Intriago that he intended to lead a provisional government to replace that headed by Mr. Moïse. The statement didn’t say how the provisional government was supposed to come about. Mr. Sanon, currently under arrest in Haiti, wasn’t available for comment.

The statement said Mr. Intriago believed the Colombians were unarmed and still awaiting permits for firearms from the Haitian police when there was a change of plans.

Now the mission was to accompany Haitian police in arresting the president, the statement said. The security team “were being requested to accompany a judge who would go along with Haitian police while the warrant was served upon President Moïse,” the statement said. A copy of the warrant, signed by Haitian judge Jean Roger Noelcius and dated Feb. 18, 2019, for the crime of murder, was supplied to Mr. Intriago on his request. Mr. Noelcius couldn't be reached for comment. There were no further details on the alleged crime.

Windelle Coq-Thelot, a former Supreme Court judge and magistrate, wanted Mr. Intriago’s assistance executing the arrest warrant, according to the statement. Ms. Coq-Thelot was fired earlier in the year along with two other justices after Mr. Moïse claimed he had foiled a coup attempt in February.

But in her letter to Mr. Intriago, she presented herself as an active judge and argued Mr. Moïse had overstayed his five-year-term—and was becoming a dictator.

Mr. Moïse’s term was meant to start in February 2016, but a runoff election was delayed and he didn’t take office until February 2017, creating a dispute over whether his five years should end in February 2021 or February 2022.

“I hereby expressly request that your company, that its members assist our Constitutional authorities, especially myself and in general the Haitian people in order to protect democracy,” she wrote in the letter to Mr. Intriago that was released by his lawyers. “I ratify, in my capacity as a Magistrate, in my capacity as a lifetime official and that I represent the people, and protected by the actions of a Judge and a Prosecutor, by the merit given to us by the Constitution, the Law and Reason that we give and will give immunity, protection and security to their actions in our favor.”

An arrest warrant was issued for Ms. Coq-Thelot’s arrest in late July. Her whereabouts is unknown.

“I firmly denounce the political persecutions of which I am subjected to at the moment,” said a tweet posted Sunday on an unverified Twitter account purporting to belong to Ms. Coq-Thelot.

Mr. Intriago’s lawyers said the U.S. government was aware of his business plan. After Mr. Sanon, the Florida-based preacher, approached him with a proposal to provide security for the solar project, Mr. Intriago had a business associate “call individuals at the US government to get assurances that the business dealings were legitimate,” they said in the statement.

“Whenever Mr. Intriago questioned the legality of providing security services for Dr. Sanon or anyone else in Haiti, [the business associate] called his FBI contacts and Mr. Intriago became confident that the United States government knew exactly what was taking place in Haiti,” the lawyers said. They didn’t indicate the identity of those contacts at the FBI.

The statement doesn’t clarify which parts of the evolving plan—which morphed from providing a security detail for a solar-panel project to arresting a sitting president—Mr. Intriago thought the U.S. government was aware of.

The FBI didn’t immediately respond to a request for comment. A State Department spokeswoman has previously said that reports the ex-soldiers were acting on behalf of the U.S. government were false.

Write to Drew Hinshaw at drew.hinshaw@wsj.com and José de Córdoba at jose.decordoba@wsj.com