MEDICINE LODGE, Kan. — Firefighters trying to snuff out the biggest wildfire in Kansas history are getting help from military helicopters — and a potential assist from looming rain or snow.

Two UH-60 Black Hawk helicopters from the Kansas National Guard were deployed Saturday in the efforts to contain the persistent prairie blazes that since Tuesday have charred at least 620 square miles in Oklahoma and southern Kansas, destroying at least two homes and some livestock. No serious human injuries have been reported.

Each helicopter has a 660-gallon bucket that will be used to dump water from local sources onto the flames, said Ben Bauman, a spokesman for the Kansas adjutant general’s office. The National Guard also was contributing a fuel tanker truck and another ground support vehicle.

Firefighters focused again Saturday on Butler County, southwest of Wichita, said Darcy Golliher, a spokeswoman for the Kansas Incident Management Team. The blaze has burned 427 square miles of that county, and only 15 percent of that fire has been contained.

The National Weather Service said the area where the fire has raged, which borders Oklahoma, was expected to get one-tenth to a quarter inch of rain or snow Saturday night or Sunday morning.

‘‘There’s still a bit of uncertainty about how much they could get,’’ said Andy Kleinsasser, a meteorologist with the weather service’s Wichita office. ‘‘Hopefully they can get a decent dousing. Anything is better than nothing.’’

The wildfire is the ‘‘largest in Kansas history and one of the largest in US history,’’ the Kansas Forest Service said in a release Friday.

Officials are trying to determine whether the fire damage meets the threshold for a Federal Emergency Management Agency disaster declaration, which would provide public assistance for damaged public infrastructure.

The fire has been persistent in Barber County, which is southwest of Wichita along the border with Oklahoma.

Earlier in the week, smoke from Kansas was reportedly detected as far away as St. Louis, hundreds of miles to the northeast.

In neighboring Comanche County, the fire was mostly contained, although crews were monitoring for flareups, said John Lehman, the Kansas county’s emergency management coordinator. He said the concern was that sparks from still-burning trees and cedars in canyons in the area’s Gyp Hills would blow up and ignite flames on the ridges.

‘‘Up on top they feel like they have it,’’ he said. ‘‘It’s looking a lot better.’’

A separate grass fire that hit near the Kansas town of Burrton, which is about 30 miles northwest of Wichita, burned about 22 square miles before it was controlled Thursday. One home was destroyed and several head of livestock were killed.

In Oklahoma, officials planned to conduct damage assessments Friday to determine how many buildings have been lost in the blaze, said Michelle Finch-Walker, a spokeswoman for the state’s Forestry Services.

‘‘Due to the extraordinary firefighting efforts yesterday and a little help from Mother Nature, we didn’t see any fire growth,’’ she said.