Moise was shot dead early on Wednesday at his Port-au-Prince home by what Haitian authorities describe as a unit of assassins formed of 26 Colombians and two Haitian Americans, plunging the troubled Caribbean nation deeper into turmoil.
National Police Chief Leon Charles told a news conference the arrested man, 63-year-old Christian Emmanuel Sanon, flew to Haiti on a private jet in early June, accompanied by hired security guards, and wanted to take over as president.
He did not explain Sanon's motives beyond saying they were political, but added that one of those in custody had contacted him upon being arrested. Sanon, in turn, contacted two other "intellectual authors" of the assassination, Charles added.
"The mission of these attackers was initially to ensure the safety of Emmanuel Sanon, but later the mission was changed...and they presented one of the attackers with an arrest warrant for the president of the republic," Charles said.
Public records online show a man with Sanon's name worked as a doctor in Florida, but it was not immediately clear if it was the same man.
Nor was it clear why Sanon would want to topple Moise, whose murder is the latest in a string of reverses for the struggling country, which has sought international help.
Washington has rebuffed Haiti's request for troops, though a senior U.S. official said on Sunday it was sending a technical team to assess the situation.
Haitian police have arrested 18 Colombians and 3 Haitian Americans, including Sanon, over the murder, Charles said. Five Colombians are still at large and three were killed, he added.
The suspected assassins told investigators they were there to arrest him, not kill him, the Miami Herald and a person familiar with the matter said earlier on Sunday.
A source close to the investigation said two Haitian Americans, James Solages and Joseph Vincent, told investigators they were translators for the Colombian commando unit that had an arrest warrant. But when they arrived, they found him dead.
The news follows reports that some of the Colombians had said they had gone to work as security personnel on Haiti, including for Moise himself.
The Miami Herald reported that the detained Colombians said they were hired to work in Haiti by Miami-based company CTU Security, run by Venezuelan emigre Antonio Enmanuel Intriago Valera.
Charles indicated that CTU had been used to hire at least some of the Colombian suspects, but gave no details.
Neither CTU nor Intriago could immediately be reached for comment.
One phone number associated with the company in public records sent calls to an answering machine that made a reference to the fictional TV character Jack Bauer, who fought terrorism in the series "24."
The recorded message ran, "Thank you for calling CTU Security. For Tony Intriago, please leave a message or send a text. For Jack Bauer, wait for the next season. Thank you for calling and have a great day."
Social media profiles that appeared to belong to Intriago included a Facebook photo showing a man in tactical gear pointing a high-powered rifle. Instagram pictures showed ammunition, guns, and people engaged in tactical training.
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Photos and X-ray images posted on social media at the weekend said to be from Moise's autopsy showed his body riddled with bullet holes, a fractured skull and other broken bones, underscoring the brutal nature of the attack.
Reuters could not independently confirm their authenticity.
Via social media, Haitians in parts of the capital Port-au-Prince were planning protests this week against the interim prime minister and acting head of state Claude Joseph.
Joseph's right to lead the country has been challenged by other senior politicians, threatening to exacerbate the turmoil engulfing the poorest country in the Americas.
On Saturday, one of Haiti's top gang leaders, Jimmy Cherizier, a former police officer known as Barbecue, said his men would take to the streets to protest the assassination.
Cherizier, boss of the so-called G9 federation of nine gangs, said police and opposition politicians had conspired with the "stinking bourgeoisie" to "sacrifice" Moise.
Gunfire rang out overnight in the capital, which has suffered a surge in gang violence in recent months, displacing thousands and hampering economic activity.