Let the battle of the war stats begin.

The U.S.-led coalition on Thursday released estimates of the violence in Afghanistan that painted a picture of improving security this summer, particularly in areas of the south where NATO has concentrated the bulk of its troops. The number of “enemy-initiated attacks” dropped 17 percent across the country from June to August compared with the same period last year, according to the NATO figures.

The data stand in contrast to a bleaker assessment released by the United Nations this week. The U.N. report said the average monthly number of “security incidents,” such as gun battles and roadside bombings, was 39 percent higher through August this year compared with the same period last year. In those eight months, the coalition noted a 2 percent drop in enemy attacks over last year.

The United Nations also reported that the number of civilians killed and wounded was 15 percent higher in the first half of this year than the same period last year.

The two batches of statistics represent strands of the competing narratives this summer in Afghanistan. The U.S. military has tended to be more optimistic that military progress was turning the tide against the Taliban, while the United Nations, nongovernmental organizations and Afghan officials have been more pessimistic about the state of the decade-long conflict.

The statistics in the two reports were difficult to compare directly because the coalition and the United Nations measure violence differently.

The coalition does not count as “security incidents” some of the things that the United Nations tallies, such as assassinations, arrests and weapons caches found, said German Brig. Gen. Carsten Jacobson, a NATO spokesman.

“Approximately 25 percent of the total U.N. security incidents are event types that ISAF does not include in its definition of security events,” Jacobson told reporters Thursday, referring to the NATO-led International Security Assistance Force. The coalition said its data cover about 80 percent of the country and focused on where troops are deployed.

Over the past several years, violence has risen in the summer months and dropped in the winter, when it is more difficult for insurgents to cross Afghanistan’s snowy mountain passes. But the trend in 2011 has been different, coalition officials said. For the first time since 2007, the months from May through August were less violent than the same months the year before, the officials said.

The greatest declines were found in NATO’s regional command southwest, which includes Helmand province, the initial focus of the 30,000 additional troops President Obama dispatched to Afghanistan. In that part of the country, enemy-initiated attacks, which include roadside bombings, gunfire and mortar attacks, dropped 39 percent from June to August this year over last year, a “marked and consistent progress,” said Lt. Col. Bret Van Poppel, who specializes in tracking statistics for the coalition.

By contrast, this category of violence showed a 15 percent increase in eastern Afghanistan this summer over the last, according to the coalition. In that area, along the border with Pakistan, “we see a continued challenge in our security situation,” Van Poppel said.

The coalition did not specify the numbers of attacks. But according to its graphics — to be published online Friday — it counted more than 3,000 enemy attacks across the country in August; there were more than 4,000 in August last year. In August 2008, about 1,000 insurgent attacks occurred.

The U.N. report put the average monthly number of security incidents at 2,108 from January to August.