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.

A year ago, McChrystal imposed new restrictions on how NATO troops fight the enemy. The rules, credited for reducing the number of civilians killed and wounded by international troops, helped win McChrystal the trust of many Afghans.

Down in the ranks, however, the rules are widely perceived as too restrictive. Some troops believe the rules cost American lives and force them to give up the advantage of overwhelming firepower to a foe who shoots and melts back into the civilian population.

Kirby said that for now, all the rules of engagement that were in place under McChrystal will remain in effect.

"Gen. Petraeus, as any new commander, has the right when he comes in to review those rules of engagement and may recommend changes to them as he sees fit," Kirby said. "But we have no indication right now that he has any intention of changing anything."

Mark Moyar, a counterinsurgency expert, said he expected that Petraeus would reassess the rules and how they were being applied.

"I think morale would not be an issue if the rules permitted success, but in many cases they have made it impossible to defeat the insurgents and to convince the population that we are strong enough to protect them," he said.

The rules don't prevent U.S. troops from calling in air support, especially in the rugged east of the country where Taliban fighters are active but the population is smaller than in the agricultural areas of the ethnic Pashtun south - the main focus of the war. But the emphasis is on caution, and officers fear career damage if they mistakenly call for air or heavy weapons support and kill civilians in the process.

Details of the rules are classified, but troops say they cannot fire on a suspected militant unless he is presenting a clear threat. Troops say, for example, if a fighting-age man emerges from a building from which they are taking fire, the soldiers cannot fire at him unless he is armed or they personally saw him drop a weapon.

On the battlefield, five international service members died on Saturday, NATO said. Two, including at least one American, were killed in two separate roadside bombings in southern Afghanistan. Two others, including one American, were killed in roadside bomb attacks in the east. That brought to 89 the number of international troops killed so far in June - already the deadliest month of the nearly 9-year-old war. The figure includes at least 52 Americans.