He spoke by phone to CNN on Sunday. Asked several times what he and those with him want, he answered in vague terms, saying that they want the federal government to restore the "people's constitutional rights."
"This refuge -- it has been destructive to the people of the county and to the people of the area," he said.
"People need to be aware that we've become a system where government is actually claiming and using and defending people's rights, and they are doing that against the people."
The group is occupying part of the Malheur National Wildlife Refuge near Burns after gathering outside for a demonstration supporting Dwight and Steven Hammond, father-and-son ranchers who were convicted of arson.
Prosecutors said the Hammonds set a fire that burned about 130 acres in 2001 to cover up poaching. They were sentenced to five years in prison.
The Hammonds, who are set to turn themselves in Monday afternoon, have said they set the fire to reduce the growth of invasive plants and to protect their property from wildfires, CNN affiliate KTVZ
The Hammonds have been clear in that they don't want help from the Bundy group.
"Neither Ammon Bundy nor anyone within his group/organization speak for the Hammond family," the Hammonds' attorney W. Alan Schroeder wrote to Harney County Sheriff David Ward.
CNN law enforcement analyst Art Roderick, a retired U.S. marshal who investigated anti-government militias for years, warned that Bundy's call for supporters to join him might "turn into a bad situation."
"What's going to happen hopefully (is) ... we don't go out there with a big force, because that's what they're looking for," he said. "The last thing we need is some type of confrontation."
He said that over the years, law enforcement has learned how to handle a situation like this; one that hasn't erupted in violence and in which a law may be broken, but there's no immediate threat to anyone's life.
The best approach now, Roderick said, is to wait the group out and to figure out how to bring a peaceful end to the situation.
The protest has prompted Harney County School District 3
to call off classes for the entire week, Superintendent Dr. Marilyn L. McBride said.
"Schools will open on January 11," she said. "Ensuring staff and student safety is our greatest concern."
'We are not terrorists'
After the march Saturday, the armed protesters broke into the refuge's unoccupied building and refused to leave. Officials have said there are no government employees in the building.
"We will be here as long as it takes," Bundy said. "We have no intentions of using force upon anyone, (but) if force is used against us, we would defend ourselves."
Ammon Bundy said that the group in Oregon was armed, but that he would not describe it as a militia. He declined to say how many people were with him, telling CNN on Sunday that giving that information might jeopardize "operational security."
The elder Bundy drew national attention last year after staging a standoff
with federal authorities over a Bureau of Land Management dispute.
"We are not terrorists," Ammon Bundy said. "We are concerned citizens and realize we have to act if we want to pass along anything to our children."
He wouldn't call his group a militia, but others are.
"I don't like the militia's methods," local resident Monica McCannon told KTVZ. "They had their rally. Now it's time for them to go home. People are afraid of them."
What the protesters want
When asked what it would take for the protesters to leave, Bundy did not offer specifics. He said he and those with him are prepared to stay put for days or weeks or "as long as necessary."
"We are using the wildlife refuge as a place for individuals across the United States to come and assist in helping the people of Harney County claim back their lands and resources," he said.
"The people will need to be able to use the land and resources without fear as free men and women. We know it will take some time."
He did not explicitly call on authorities to commute the prison sentences for the Hammonds, but he said their case illustrates officials' "abuse" of power.
"Now that people such as the Hammonds are taking a stand and not selling their ranches, they are being prosecuted in their own courts as terrorists and putting them in prison for five years," Bundy said.
He said the Malheur National Wildlife Refuge has taken over the space of 100 ranches since the early 1900s.
"They are continuing to expand the refuge at the expense of the ranchers and miners," Bundy said.
He also said Harney County, in southeastern Oregon, went from one of the state's wealthiest counties to one of the poorest.
CNN has not independently corroborated Bundy's claims.
"I want to emphasis that the American people are wondering why they can't seem to get ahead or why everything is costing more and you are getting less, and that is because the federal government is taking and using the land and resources," Bundy said.
What the feds say
Acting U.S. Attorney Billy J. Williams of Oregon gave a starkly different perspective on the arson case.
His office declined to comment on the situation at the wildlife refuge Saturday, but it cited an opinion piece written by Williams in the Burns Times Herald
last month defending the federal prosecutors' actions in the Hammonds case.
"Five years ago, a federal grand jury charged Dwight and Steven Hammond with committing arson on public lands and endangering firefighters," Williams wrote for the newspaper. "Steven Hammond was also found guilty of committing a second arson in 2006."
The prosecutor said witnesses saw the Hammonds illegally slaughter a herd of deer on public land.
"At least seven deer were shot with others limping or running from the scene," Williams wrote.
He said a teenage relative of the Hammonds testified that Steven Hammond gave him a box of matches and told him to start the blaze. "The fires destroyed evidence of the deer slaughter and took about 130 acres of public land out of public use for two years," the prosecutor wrote.
Williams also disputed the notion that the Hammonds were prosecuted as terrorists, as Bundy suggested.
"The jury was neither asked if the Hammonds were terrorists, nor were defendants ever charged with or accused of terrorism," Williams wrote. "Suggesting otherwise is simply flat-out wrong."