Martinez said two people have been detained in the investigation for questioning. But he added that police have yet to establish a motive in the crime.
Faull was found with a gunshot wound to his head inside his two-story home north of San Pedro, a town on the island of Ambergris Caye, Martinez said. The housekeeper discovered the body Sunday morning and called police. Martinez said that no charges had been filed in the case.
McAfee told Wired that whoever shot Faull may have been gunning for him instead and mistakenly killed his neighbor.
San Pedro Mayor Daniel Guerrero said that Faull had given the town council a letter complaining that McAfee's dogs were running loose, chasing cyclists and attacking people and that his security guards trespassing on other homeowners' property.
Still, Guerrero said there wasn't enough evidence for him to say McAfee is a suspect.
"Both of them were my friends. It's hard. It's something that has shocked the community", Guerrero said.
Faull's family said in a statement that the Orlando, Fla. man, owner of a construction business, had just finished rebuilding his Belize home and was planning to offer it as a vacation rental while he sailed the seas.
"Losing Greg leaves a hole in our hearts and our lives. We urge law enforcement authorities in Belize and internationally to bring those responsible to justice quickly," the statement said.
Belize police said they believe McAfee is still in Belize, but would contact authorities in the United States, Mexico and Guatemala if there are signs he has left the country.
The AP tried unsuccessfully to contact McAfee by email.
McAfee sold his stake in the anti-virus software company that is named for him in the early 1990s and moved to Belize about three years ago to lower his taxes.
He told The New York Times in 2009 that he had lost all but $4 million of his $100 million fortune in the U.S. financial crisis.
Last April, Belize police raided McAfee's home looking for drugs and guns. McAfee said officers found guns, which he said were legal, and he was released without charge after being detained for a few hours.
He also has another property in mainland Belize, a compound of thatched-roof homes near the Mexico border.
One resident of the island told the AP that Faull had complained about McAfee's behavior, and others said the former software executive was hard to befriend.
"His physical appearance doesn't really inspire you to go over and make friends with him. He's a little scruffy looking," said real estate agent, Bob Hamilton.
Wired reported that McAfee said his dogs were poisoned on Friday night and that he blames the deaths on Belize authorities, not Faull, who complained about them. Police spokesman Martinez said that officers didn't find any dogs when they arrived at McAfee's San Pedro home and that an employee there said the dogs had died and McAfee had buried them.
Police said Faull's computer and phone were missing, but there were no signs of forced entry at his home. Police reported finding a single 9-mm shell casing and said it appeared Faull was killed between late Saturday and Sunday morning, which was a rainy night on the Caribbean island. Faull was last seen at 10 p.m. Saturday.