Four men have been accused in Utah of raping a nine-year-old child while her mother smoked methamphetamine, in a case that has prompted a furious outcry and appeals for calm.

According to a statement by the Uintah County Sheriff's Office, the rape took place on March 27 as the mother was visiting friends in the town of Vernal, east of Salt Lake City, and went to the garage to smoke drugs while her daughter slept on a couch.

"During that time, the child was taken into another room in the home where she was raped by the four men," the sheriff's office said in a statement.

The men, who were living temporarily at the house, were later arrested and charged with rape and sodomy.

They made their initial appearance in court on Tuesday and are scheduled for a bail hearing on April 11.

The case has led to a public outcry in the small town and beyond, with some calling in social media postings for the four men to face a firing squad or be hanged.

The calls for vigilante justice prompted the sheriff's office to appeal for calm on Monday in a statement on its Facebook page.

"The interest and concern over the case of victimization of a nine year old girl in our county has been overwhelming and unprecedented," the statement said. "Occasionally, there are incidents that we face that are shocking to the conscience, and this case has certainly been one of those for us all."

G. Mark Thomas, the county attorney, said the case was particularly disturbing as it involved the gang rape of a child.

"We are always concerned when a child is abused (but) this is particularly heinous in that she was abused by four adults in rapid succession in a very demeaning way," he told AFP. "This is a first reported incident of multiple adults simultaneously abusing a child of this age."

According to court documents, the four men took turns raping the child over a 30-minute period before putting her back on the couch and threatened to kill her if she told anyone.

The mother said she found her daughter upset, with her dress "pulled up past her waist" when she returned from the garage and took her home.

She called police the next day after her daughter told her of the rape.

Authorities said the child was taken to hospital and has been placed in government custody.

The four alleged attackers -- Larson RonDeau, 36, Josiah RonDeau, 20, Jerry Flatlip, 29 and Randall Flatlip, 26 -- face up to life in prison if convicted.