FBI agents on Wednesday surrounded the last few demonstrators holed up at a federal wildlife refuge in Oregon, in a move suggesting that the weeks-long armed siege might be approaching a climax.

The remaining four said they will turn themselves in on Thursday morning, local media including The Oregonian reported, after negotiations between the occupiers and the FBI on what was the 40th day of the tense standoff.

The siege at the Malheur National Wildlife Refuge began on January 2 when protest leader Ammon Bundy and 30 armed followers, most of them from other US states, took over the site to demonstrate against federal land policies.

FBI agents were deployed at barricades "immediately ahead of and behind the area where the occupiers are camping," the FBI said in a statement, as it closed on the dogged last protesters.

"It has never been the FBI's desire to engage these armed occupiers in any way other than through dialogue, and to that end, the FBI has negotiated with patience and restraint in an effort to resolve the situation peacefully," said Greg Bretzing, head of the FBI's Portland office.

"However, we reached a point where it became necessary to take action in a way that best ensured the safety of those on the refuge, the law enforcement officers who are on scene, and the people of Harney County who live and work in this area."

The FBI said that it moved in after one of the remaining occupiers drove an all-terrain vehicle beyond the makeshift barricades set up by the protesters.

FBI agents tried to approach the driver but he sped back to the refuge compound.

The Oregonian tweeted that the FBI told the occupiers that they would not escalate the situation in what was left of Wednesday, but were not leaving the scene either.

Bundy, who was among a dozen people arrested late last month, has repeatedly called for the last four holdouts to call off the movement and leave peacefully.

Among those refusing to surrender is David Fry, who has vowed to stand his ground.

The band of original occupiers included Jon Ritzheimer, an Arizona man who gained notoriety for organising anti-Islam demonstrations, and LaVoy Finicum, who acted as spokesman for the group and was killed by police after he drove out of the refuge and tried to run a roadblock.

Ritzheimer surrendered to police in Arizona late last month.

Gunmen took over the remote wildlife refuge to protest at the jailing of two local ranchers, Dwight Hammond and his son Steven, who were convicted of arson.