Bundy was arrested Tuesday night during a traffic stop. Another protester was shot and killed during the same stop.
"To those remaining at the refuge, I love you. Let us take this fight from here. Please stand down. Go home and hug your families," Bundy said in a statement. "This fight is ours for now in the courts. Please go home."
"We need to step back. Somebody died yesterday," attorney Mike Arnold told reporters. "Mr. Bundy wants everybody to remember that somebody died, and this is not just about him right now."
Arnold spoke after Harney County Sheriff David Ward blamed the occupiers for the death of the outspoken protester. Although authorities have not named the person who was shot and killed, others have identified him as LaVoy Finicum.
"Multiple agencies put a lot of work into this to put the best tactical plan that they could to arrest them peacefully," said Ward. "(The death) didn't have to happen. We all make choices in life. Sometimes our choices go bad."
A law enforcement official told CNN that officers opened fire when Finicum reached toward his waistband, where he had a gun.
With their leader arrested and a fellow protester killed, an unknown number of demonstrators have indicated they'll continue their weekslong armed occupation. The FBI tried to assert more control Wednesday, setting up checkpoints on roads heading to and from Malheur National Wildlife Refuge.
"We don't arm up and rebel," said Ward, urging everyone involved in the occupation to "move on."
"We work through the appropriate channels. This can't happen anymore. This can't happen in America, and it can't happen in Harney County," the sheriff said.
Occupiers who remained told a CNN crew near the headquarters building that they intended to stay there. It wasn't immediately clear how many remained.
The checkpoint into the refuge had high security Wednesday. A CNN crew was instructed to stop. A sniper aimed at vehicles as a reporter was told to get out, and asked for ID and whether she had any weapons on her. FBI agents got into the cars by themselves and drove the vehicles through the checkpoint to the other side.
Oregon Public Broadcasting (OPB) radio's John Sepulvado, reporting on refuge grounds outside the occupied building, said that occupiers told him they were prepared to die.
"I just spoke to the new leaders -- including Jason Patrick -- They say that 5-6 (people) had a meeting, and by consensus they decided to stay," Sepulvado wrote Wednesday morning on Twitter.
The decision to stay came on the 26th day of the occupation of the refuge building in eastern Oregon, which armed demonstrators took over January 2, in part to protest the sentencing of two ranchers and what they call government overreach when it comes to federal lands.
It came the day after Finicum's death -- a killing that his fellow demonstrators called murder.
Protest leaders were on their way to a community meeting set up by local residents when authorities attempted to pull them over, according to a law enforcement official who described the dramatic showdown.
One vehicle stopped, but the other, driven by Finicum, took off at high speed, the source said. With police in hot pursuit, Finicum tried to leave the main road and drove into a snowbank.
He emerged from the vehicle and was ordered to surrender, said the source. That's when, according to the source, Finicum reached toward his waistband, where he had a gun.
Officers opened fire and Finicum was killed. Bundy's brother, Ryan Bundy, suffered a light wound on his arm.
Occupiers: 'A patriot has fallen'
Finicum was one of the most vocal occupiers who took over the refuge building near Burns.
Earlier this month, the father of 11 told CNN he did not want to die -- but would never go behind bars.
"I'm just not going to prison," Finicum said. "Look at the stars. There's no way I'm going to sit in a concrete cell where I can't see the stars and roll out my bedroll on the ground. That's just not going to happen. I want to be able to get up in the morning and throw my saddle on my horse and go check on my cows. It's OK. I've lived a good life. God's been gracious to me."
News of Finicum's death quickly reached the protesters still holed up at the refuge building.
"It appears that America was fired upon by our government," the occupiers said on the Bundy Ranch Facebook page
. "One of liberty's finest patriots is fallen. He will not go silent into eternity."
The occupiers claimed Finicum had his hands in the air when he was shot.
A representative from the Joint Information Command Center in Harney County said authorities had no comment on the claim that Finicum had his hands up. He said more information would be released.
Cliven Bundy said Finicum died supporting his beliefs.
"He was a wonderful man," he told KTNV
. "He was a student of the Constitution. He was interested in freedom, and I think he gave his life where he felt it was best."
In all, police arrested eight people Tuesday linked to the wildlife refuge takeover: five in the traffic stop on U.S. Highway 395; two others in Burns; and one in Arizona, the FBI and Oregon State Police said.
The five arrested at the traffic stop were Ammon Bundy, Ryan Bundy, Brian Cavalier, Shawna Cox and Ryan Waylen Payne.
The two arrested in Burns were Joseph Donald O'Shaughnessy and Peter Santilli.
Protester Jon Ritzheimer, who previously made headlines for leading an anti-Islam protest
in Arizona, turned himself in to police in Peoria, Arizona, FBI spokesman Kurt Remus said.
All eight face a federal felony charge of conspiracy to impede officers of the United States from discharging their official duties through the use of force, intimidation or threats, authorities said.
According to charging documents, a source told a Harney County officer that the group had explosives and night vision goggles, and weapons, and that "if they didn't get the fight they wanted out there they would bring the fight to town."
Ammon Bundy and others started out protesting the sentencing of Dwight Hammond and his son Steven, ranchers who were convicted of arson on federal lands in Oregon.
But a January 2 march
supporting the Hammonds led to the armed occupation of the refuge, with protesters decrying what they call government overreach when it comes to federal lands.
Since then, the occupiers have turned the refuge into their own -- changing the sign in the front and tearing down a fence they claimed harmed the livelihood of a rancher. But that rancher told The Oregonian
he didn't ask the occupiers to tear down the public fence -- in fact, he was upset by it.
Ammon Bundy has said that while the armed protesters don't want violence, they would be ready to defend themselves if necessary.
But with the leader arrested, it's not clear what will happen next.
On Twitter, Gov. Kate Brown stressed that she was doing everything in her power to end the occupation.