The federal government has cut the size of its police force in Indian country, reduced financing for law enforcement and begun fewer investigations of violent felony crime, even as rates of murder and rape there have increased to more than 20 times the national average, according to data.

The data, much of it contained in recently released Justice Department reports, underscores a reputation for chronic lawlessness on Indian reservations, where unchecked crime has for years perplexed federal agencies, which are largely responsible for public safety on Indian lands.

As one illustration of the profound increase in violence in recent years — despite generally declining crime in much of the rest of the nation — F.B.I. crime data reports that the number of reported rapes on the Navajo reservation in the Southwest in the last several years has eclipsed those in nine of America’s 20 largest cities, even though there are only 180,000 people on the reservation.

The reservation’s 374 reported rapes in 2009, for example, outpaced even the total for Detroit, for decades among the nation’s most violent cities, which had 335 rapes that year.