The auction of a gun belonging to a Florida man who shot and killed black teenager Trayvon Martin - triggering protests across the US - has apparently been halted.

George Zimmerman said he planned to sell the gun he used in an auction on Thursday and to spend some of the proceeds to challenge gun control policies, according to the auction website.

The one-day auction was to begin at 11am EST, with bids to start at $US5,000.

But the listing disappeared from the site soon after its scheduled start.

Representatives for the website offering the handgun for sale, Gunbroker.com, did not immediately respond to questions about why the listing came down and whether the gun had been sold.

Zimmerman, had described the gun as "a piece of American history," according to the website.

US Department of Justice recently returned to Zimmerman the Kel Tec 9mm pistol that he had used to kill the unarmed Martin on February 26, 2012.

Daryl Parks, a lawyer for Martin's family, called the potential gun sale offensive in a phone interview but said the family remain focused on their work advocating against gun violence.

"It's a distraction, and it shouldn't be a distraction to what we're doing," said Parks, who also serves as chairman of the Trayvon Martin Foundation.

Zimmerman was acquitted of second-degree murder and manslaughter charges in the incident, which sparked civil rights rallies and brought scrutiny of Florida's controversial "stand your ground" law.

Zimmerman, who was a neighbourhood watch volunteer at the time, has maintained that the shooting was in self-defence.

Martin's family said the teenager was simply passing through the residential area on his way home from a convenience store.

President Barack Obama said after Zimmerman's acquittal that Martin "could have been me, 35 years ago" and urged Americans to understand the pain African Americans felt over the case.

"George Zimmerman" quickly became the top trending term on Twitter in the United States on Thursday, with many users on the social media site expressing shock and revulsion.

"The only people worse than George Zimmerman are the people who bid on that gun," tweeted journalist and columnist Lyz Lenz.

On the auction website, Zimmerman had said he planned to use part of the proceeds to fight Black Lives Matter, a movement that grew out of the incident, as well as to counter "violence against law enforcement officers."

Proceeds would also go towards fighting Democratic presidential hopeful Hillary Clinton's "anti-firearm rhetoric," he said.

"I am honoured and humbled to announce the sale of an American firearm icon," he said on the site.

He also said in the description that "many have expressed interest in owning and displaying the firearm, including The Smithsonian Museum in Washington D.C."

The Smithsonian replied on Twitter that it had never expressed interest in the gun, and had "no plans to ever collect or display it in any museums."

In a phone interview with a local broadcaster on Wednesday, Zimmerman dismissed criticism of the auction.

"They're not going to be bidding on it, so I couldn't care less about them," he told Orlando TV station WOFL.

"What I've decided to do is not cower," he said. "I'm a free American. And I can do what I like with my possessions."