MONTPELIER, Vt. — About 16 farm elk that have been on the run since they escaped from their enclosure in Derby last weekend hopefully can be recaptured, but if not they will have to be shot because they could pose a threat to people and other animals, state Fish and Wildlife Department officials said.

There is no set time limit on how long officials will give to recapture the elk, which are believed to be traveling in a group of about a dozen and another group of about four, department Commissioner Louis Porter said Friday. State officials have been working with owner Doug Nelson to recapture them, he said.

“If we are not able to do that we are talking to the owner, to Doug, about shooting them,” Porter said. “Obviously our best option, our hope, would be to get them back alive. But if they are posing a risk to people or a disease risk to wildlife we might have to take other measures.”

Porter said captive deer-like animals have escaped their fenced-in areas in Vermont in the past but never in such large numbers.

The elk were being held in an enclosure belonging to Nelson when a gate was left open on Sunday. Soon afterward the elk were spotted roaming the area. One photograph showed the elk swimming across Salem Lake in Derby , a Canadian border town.Porter said the primary worry is public safety. The elk could wander onto a highway and be hit by a vehicle, or they could run into a person.

They also could cause property damage by running through fences. And they could pose a threat, however slight, of introducing chronic wasting disease into Vermont’s deer herd.

Porter and Scribner said there was little worry the elk could go wild and establish a herd in the region.