Neighbors earlier had correctly identified the grandmother as Martha Johnson, the newspaper said.
Johnson and the three children, victims of "violent deaths," were found Sunday, FBI spokesman Kyle Loven said.
"We are looking at those deaths as homicides," Loven said Monday.
The death of a man whose body was found in nearby Parshall, on an Indian reservation, also is being investigated "in connection" with the New Town homicides, Loven said.
"We are not looking at that death as a homicide," he said.
The newspaper said Loven would not say whether it appeared to be a murder-suicide.
The FBI is leading the investigation because New Town and Parshall are on the Fort Berthold Reservation.