Violent crime rose in the United States in 2012 for the first time in six years, led by an increase in major crimes in large cities, according to preliminary data released Monday by the F.B.I.

The largest increases took place in cities with populations of between 500,000 and one million people, where violent crime rose by 3.7 percent, including a 12.5 percent spike in murder rates, according to the data.

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.

In 2011, for instance, the nation’s rate of violent crime rate fell by 3.8 percent after having dropped by 6 percent in 2010 and 5.5 percent in 2009, according to F.B.I. data.

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.

In fact, crime levels have been dropping so much for so long that criminologists had been left guessing the reasons — and where it might end.

“We probably now have answered the question of how low it can go, and we may be bouncing off the bottom now,” said Dennis Jay Kenney, a professor at John Jay College of Criminal Justice in New York.

But Dr. Kenney added a note of caution, saying that seeking to pin a reason for a single year’s increase in serious crime was inadvisable. “We probably need another year to tell if we’ve got a pattern here,” he said.

Joseph Pollini, another John Jay College professor, said that one possibility was that there were fewer police officers on patrol in some metropolitan areas that have cut spending sharply in recent years because of the recession.

“You’re dealing with depleted police resources,” he said of budget cuts that have caused a reduction in the size of nearly every urban police department.

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.

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