They took over the Malheur National Wildlife Refuge over the weekend and have showed no signs of leaving.
"To members of the Burns-Paiute Tribe and residents of Harney County who seek a return to normal life: I hear you, and I agree that what started as a peaceful and legal protest has become unlawful," the governor said in a statement Thursday.
"It was instigated by outsiders whose tactics we Oregonians don't agree with. Those individuals illegally occupying the Malheur Wildlife Refuge need to decamp immediately and be held accountable."
Also on Thursday, Harney County Sherrif David Ward met with protest leader Ammon Bundy.
The plan is for the sides to talk again on Friday.
There's so far been no evident police presence outside the snowy, desolate wildlife refuge in southeast Oregon.
"He gave us some things to think about and we're going to think about those, and we'll let you know," Bundy said after the meeting, which lasted less than 10 minutes.
"Until we know and understand that the people are going to end up on top here, we plan on staying," he said.
When pressed by a reporter Wednesday, Bundy said, "Enough is enough when there's actual action that is happening."
Bundy spoke about the case of two local ranchers, Dwight and Steven Hammond
, who have distanced themselves from the occupiers.
The father and son 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
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 claims the two ranchers were targeted for not selling land to the government.
"We feel like we need to make sure that the Hammonds are out of prison, or well on their way," he told reporters. "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."