By Idrees Ali

WASHINGTON (Reuters) - The Afghan government lost control or influence between May and August over two percent of the territory it controlled, the U.S. government's top watchdog on Afghanistan said in a report on Sunday, a sign of the precarious security situation in the country and challenges posed by the Taliban and other militant groups.

Fifteen years after the United States invaded Afghanistan to topple the Taliban rulers who had harbored al Qaeda militants who attacked the United States, the Taliban have made major gains and are estimated to control more territory than at any time since 2001.

The report, published by the Special Inspector General for Afghanistan Reconstruction (SIGAR), said the area under Afghan government "control or influence" had decreased to 63.4 percent by the end of August from 65.6 percent near the end of May, based on data provided by U.S. forces in Afghanistan.

That number is lower than what senior U.S. officials have cited in the past.

"We believe the Afghans control or influence 68 to 70 percent of the population," General John Nicholson, the commander of U.S. and NATO forces, told a September press briefing.

About a third of the country is either under insurgent control or in risk of coming under it, posing a challenge for female education, the report said.

"In these areas, the Taliban seek to punish women who work or study outside the home," the report said.

The Taliban have challenged Afghan security forces for a number of key cities in the past few months, including Kunduz, which was overrun by the militants last year but eventually regained by the government.

The report said that from January to August, more than 5,500 members of the Afghan security forces have been killed.

Officials have voiced concern over the casualty rate, attributing it to more Taliban successes on the battlefield.

Despite the high casualty rate, the report cited a NATO survey in which 91 percent of Afghan National Army recruits surveyed said they were satisfied with their pay.

The survey, conducted from December 2015 to May 2016 found that 92 percent of recruits expect that if they are killed, their families will be taken care of.

(Reporting by Idrees Ali; Editing by Nick Zieminski)