American troops in Afghanistan will step up offensive operations this winter because insurgents are increasingly staying in the country to prepare for spring attacks, a U.S. commander told The Associated Press.

Maj. Gen. Jeffery J. Schloesser said a 40 percent surge in violence in April and May was fueled in part by militants preparing stores of weapons during the winter, which generally is a slow period for fighting, particularly in snowy Afghan mountainous areas.

"If we don''t do anything over the winter the enemy will more and more try to seek safe haven in Afghanistan rather than going back to Pakistan ," Schloesser said.

U.S. and NATO officials say militants cross into Afghanistan from Pakistan , where they rest, train and resupply in tribal areas along the frontier where the Pakistani government has little sway.

Schloesser estimated 7,000 to 11,000 insurgents operate in the eastern part of Afghanistan that he oversees — a far higher estimate than given by previous U.S. commanders.