Kabul, Afghanistan ? America’s top military officer assured President Hamid Karzai on Saturday that newly chosen NATO commander Gen. David Petraeus would pursue the policies of his ousted predecessor, whom the Afghan leader warmly praised for reducing civilian casualties.

Karzai’s emphasis on preventing civilian deaths and injuries could make it difficult for NATO to relax rules of fighting that some U.S. troops say give the battlefield advantage to the Taliban. For now, however, no changes have been proposed, said a spokesman for visiting Adm. Mike Mullen, chairman of the Joint Chiefs of Staff.

During a 45-minute meeting with the Afghan leader, Mullen explained the events that surrounded President Barack Obama’s decision to dismiss Gen. Stanley McChrystal, the commander of both U.S. and NATO forces. McChrystal resigned after he and his aides were quoted in Rolling Stone magazine making disparaging remarks about top Obama administration officials guiding the civilian mission in the war.

Mullen, who spent just a half-day in Kabul, also met with U.S. Embassy officials and had a video teleconference with regional commanders in the field. To both sides, Mullen stressed the importance of a good “lash up” between often strained civilian and military efforts to beat back a resurgent Taliban and extend the Karzai government’s control beyond Kabul.

“He stressed to President Karzai that absolutely nothing will change about our commitment to the struggle there, to the strategy,” said Capt. John Kirby, a spokesman for Mullen.

Mullen then flew to neighboring Pakistan, where he repeated the message to President Asif Ali Zardari and Chief of Army Staff Gen. Ashfaq Parvez Kayani.

Mullen’s trip, which was scheduled before McChrystal’s dismissal, took on a different tone after the change. Afghan leaders and some U.S. allies in the war worried that McChrystal’s firing could disrupt the counterinsurgency strategy at a critical juncture in the war. But they were relieved when Obama chose Petraeus, McChrystal’s boss who helped author the plan, to replace him.

Mullen stressed at the meeting that Petraeus had been involved in developing the strategy from the beginning and was attuned to the challenges in Afghanistan.

The two talked briefly about the ongoing security operation in Kandahar, a hotbed of insurgent activity, Kirby said. Karzai lauded McChrystal, saying he was able to “reduce civilian casualties, create good cooperation between the Afghan and international forces and strengthen and develop the Afghan forces,” according to a statement from the Afghan presidential palace.