MADISON, Wis. — A North Dakota man was charged Thursday with three counts of first-degree homicide in the deaths of his three young daughters in northwestern Wisconsin.

Aaron Schaffhausen, 34, of Minot was arrested after police discovered the bodies of 11-year-old Amara, 8-year-old Sophie, and 5-year-old Cecilia Schaffhausen in the home they shared with their mother in River Falls on Tuesday.

Authorities have not said how the girls were killed, but when police entered the home they noted the first-floor gas fireplace was on and the basement smelled of a flammable liquid they have yet to identify.

Investigators said Aaron Schaffhausen unexpectedly contacted the girls’ mother — his former wife — on Tuesday and asked for an unplanned visit with the children. The mother, who wasn’t home, agreed and when Schaffhausen showed up at the house, the girls’ baby sitter left.

Schaffhausen later called the mother, Jessica, and told her he had hurt the girls. She called police en route to the house.

No one was home when police arrived at the house and found the bodies.

Schaffhausen turned himself in late Tuesday afternoon and was being held at St. Croix County jail.

Circuit Judge Howard W. Cameron set bail at $2 million Thursday. He is due back in court July 24 for a preliminary hearing. His attorney, listed in court records as public defender John Kucinski, didn’t immediately return a telephone message Thursday.

An announcement in The State Journal-Register shows Aaron Schaffhausen and Jessica Schaffhausen married in 2000. Court records show they divorced in January.

River Falls Police Chief Roger Leque has said records show what the chief called a “harassment incident’’ at the house in March 2012 in which the father threatened to harm at least one of the girls. But the chief said police were unaware of any restraining orders.

The house stands in a newer subdivision on the east side of River Falls, a city of 15,000 people about 30 miles east of the Twin Cities.