One them is Ammon Bundy, the 40-year-old son of Nevada rancher Cliven Bundy, who is well-known for anti-government action.

He spoke by phone to CNN on Sunday at 8 a.m. ET. 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 inside 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. The father and son were sentenced to five years in prison.