"There is a time to go home. We recognize that. We don't feel it's quite time yet," he said.
"We feel like we need to make sure that the Hammonds are out of prison, or well on their way. We need to make sure that there is some teeth in these land transfers, and also that those who have committed crimes ... those are exposed as well."
Bundy was referring to two local ranchers, Dwight and Steven Hammond. The father and son, who have distanced themselves from the protest group, were convicted of arson and given five-year prison sentences.
The Hammonds, who turned themselves in to authorities on Monday, have said they started a fire in 2001 to reduce the growth of invasive plants and to protect their property from wildfires, CNN affiliate KTVZ-TV reported. But prosecutors said the Hammonds torched about 130 acres of public land in an attempt to cover up the poaching of deer on federal property.
Bundy has said the two ranchers were targeted for not selling land to the government.
When pressed by a reporter Wednesday on when protesters would leave, Bundy said, "Enough is enough when there's actual action that is happening.
"And when things are actually transpiring, and we'll know when that happens," he said.
Bundy: FBI planning a raid
Late Tuesday, Bundy said he's been told the FBI has obtained five arrest warrants and planned to raid the property, an allegation federal or local law enforcement did not confirm.
The protest leader didn't name the source of his information. He said he talked to an unnamed "commissioner."
According to Bundy, the source said authorities were gathering "their equipment and their goons" at a local high school, where classes have been suspended, and "they were planning on coming in and raiding the refuge."
CNN asked the FBI about the possible existence of such warrants, but the bureau referred all questions to local authorities.
The Harney County Joint Information Center said it had no information on arrest warrants and that it was still working for a peaceful resolution to the occupation.
'Armed protesters don't belong here'
There has been no evident police presence outside the snowy, desolate wildlife refuge in southeast Oregon since the occupiers took over the main building on Saturday.
Reporters, however, have come and gone easily and recorded statements from the group of about 20 people.
Bundy has been the most vocal to spread the message that the federal government has too much power and the U.S. Bureau of Land Management controls too much land.
Bundy's demand amused Charlotte Rodrique, chairwoman of the Burns Paiute Tribal Council, a Native American tribe that used to spend winters on the wildlife refuge land.
"For them to come in and say we're going to give it to the rightful owners -- I'm laughing," she said Wednesday at a news conference.
She said the tribe doesn't support the occupation of the refuge.
"Armed protesters don't belong here. By their actions they are desecrating one of our sacred sites," she said.
Wait and see
The FBI, which is leading the investigation, hasn't specified what it will do.
"The FBI is working with the Harney County Sheriff's Office, Oregon State Police and other local and state law enforcement agencies to bring a peaceful resolution to the situation at the Malheur National Wildlife Refuge," the agency's Portland office said.
Law enforcement appears to be waiting out the protesters.
"There is no real reason, at this point, to go in. And the FBI knows that," said Steve Moore, a retired supervisory special agent for the FBI.
He said federal authorities have learned that lesson the hard way. Take, for example, the deadly confrontation at the Branch Davidian compound in Waco, Texas, in 1993.
"A hundred people died in that," Moore said. "It was a suicide; however, it was provoked by the FBI intervention."