Belize police have said they want to question McAfee, who they describe as a "person of interest" in the slaying of fellow American Gregory Viant Faull. Faull, 52, was shot to death over the weekend on the Caribbean island where both men lived.
Prime Minister Dean Barrow said McAfee was only wanted for questioning and should report to authorities.
Barrow also expressed doubts about McAfee's mental state: "I don't want to be unkind to the gentleman, but I believe he is extremely paranoid, even bonkers."
McAfee, 67, who had a run-in with police earlier this year, told The Associated Press in a telephone interview from an undisclosed location that he didn't kill Faull, though he acknowledged he had differences with the dead man.
"I barely knew him, I barely spoke ten words to him in the last three years," McAfee said, speaking on a cellphone. "Certainly he was not my favourite person and I was not his."
"He was a heavy drinker and an annoyance. But the world is full of annoyances; if we killed all of our annoyances, there would be nobody left," McAfee said.
Other expat residents of the island of Ambergris Caye, where San Pedro is located, have described Faull, the owner of a construction business in Orlando, Florida, as peaceful and well-liked.
The dispute apparently involved several dogs that McAfee kept at his beachside villa and that drew complaints from neighbours. McAfee said that four of his dogs were poisoned late last week, but that he didn't initially suspect Faull of having killed them, though he knew Faull didn't like the dogs.
"He did threaten to shoot them once or twice," McAfee said of Faull, adding that his neighbour was "always angry at them."
But he said he now believes government agents or police poisoned the dogs.
"My assumption was it was some kind of government action again. This is more harassment - that was the first thing that went through my mind, and still is going through my mind. What else could it have been?" he said.
Faull was found with a gunshot wound to his head inside his two-story home north of San Pedro. The housekeeper discovered the body Sunday morning and called police.
Raphael Martinez, spokesman for Belize's Ministry of National Security, said no charges had been filed in the case, but urged McAfee to turn himself in, accompanied by someone else, if he felt safer that way.
But McAfee said he feared that Belize's notorious Gang Suppression Unit, the GSU, a paramilitary-style squad that has been accused of rough treatment and that raided another property McAfee owns in Belize in April, would beat him and he would later die in custody.
"The GSU will do what the GSU does, beat me soundly until I confess to a multitude of sins, including I guess the murder of Jimmy Hoffa, and then just execute me," McAfee said.
He accused authorities of detaining his friends and associates in a bid to pressure him to turn himself in.
"Of course, and it's almost working," McAfee said. "I'm sitting here, the young woman who is with me now and who has been by my side, and trying to keep me upbeat through this, I said, 'You know, I'll just call and say I'll turn myself in, just let these people go.' And she said, 'Absolutely not, they will kill you.'"
"I keep moving constantly, sir ... and I keep changing telephones constantly, this phone will expire shortly," he said.
McAfee, the creator of the McAfee antivirus program, has led a life of eccentricity since he 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. However, a story on the Gizmodo website quoted him as calling that claim "not very accurate at all."
Last April, Belize police and the GSU raided McAfee's home looking for drugs and guns. McAfee said then that officers found guns, which he said were legal, and he was released without charge after being detained for a few hours.
He has said this week that he hid in the sand with a piece of cardboard over his face to help him breathe when police raided his beachside villa Sunday after Faull's body was found.
There were still a couple of dogs at the villa Wednesday, along with a sign on the fence outside the property reading, "Never mind the dogs. Beware of Owner," together with a drawing of a hand holding a smoking pistol.
San Pedro Mayor Daniel Guerrero said Faull had given the town council a letter complaining that McAfee's dogs were running loose, chasing cyclists and attacking people and that McAfee's security guards trespassing on other homeowners' property.
Still, Guerrero said there wasn't enough evidence for him to say McAfee is a suspect.
A shopkeeper whose store is near the two men's houses said several gunshots were heard at McAfee's villa over the weekend. The shopkeeper, who did not want to be quoted by name for fear of retaliation, said the gunshots came around the same time the dogs were poisoned and speculated they may have come from someone putting the animals out of their misery.
McAfee repeated his belief that Faull's killers may have actually been looking to kill him.
"When I heard about it, the first thing I though was, 'Oh my God, they were attempting to get me and they got the wrong white man.' All white men are the same here," he said.
Asked if he would turn himself over to authorities of another country, he said: "Absolutely. If it was not a Belizean authority I would indeed, but only on the condition they not turn me into the Belizean authorities after they have questioned me."
"That's the problem, because in turning myself over to the FBI, then the Belizeans now know where I am," he said. "The FBI has limited authority in another country."
"I am innocent of everything that they're accusing me of, except probably foolishness for staying here in the country, although I still intend to stay," McAfee added. "I'm not going to leave this country. I love this country. This is my home."
Associated Press writer Mark Stevenson reported this story from Mexico City and Jose Osorio reported in San Pedro, Belize.