The nation’s largest cities, those with more than one million people, also had upturns in violent crimes, though at more modest rates. The largest cities had a 1.4 percent increase in violent crime, including 1.5 percent for murders and 3.2 percent for rapes, according to the statistics.

Over all, the nation’s violent crime rate ticked up by 1.2 percent in 2012 after years of steep declines.

The last year in which violent crime rose nationally was 2006, when the rate went up by 1.9 percent. Before that, from 1996 to 2005, violent crime had declined by 17.6 percent, according to the F.B.I. figures.

Among the big cities where violent crime increased was Indianapolis, with a population of 840,000.

While murders there rose only modestly — the 101 recorded in 2012 were five more than in 2011 — there were nearly 780 additional violent crimes in the city, led by 5,967 aggravated assaults. That figure, according to the F.B.I. data, represents some 700 more aggravated assaults than in 2011.

Memphis, with a population of 657,000, had an increase of more than 1,000 violent crimes — 11,505 in 2012 compared to 10,338 in 2011. That included a jump in the number of murders to 133 from 117.

While Detroit, with 707,000 residents, saw a drop in its violent crime rate, murders in the city increased to 386 from 344. In New York, where there was a small increase in violent crime, murders dropped by about 20 percent to 419, the lowest number in more than half a century.