MARJAH, Afghanistan - The top U.S. and NATO commander in Afghanistan crisscrossed the country Saturday, making a Christmas visit to coalition troops at some of the main battlefronts in a show of appreciation and support in the 10th year of the war against the Taliban.

Gen. David H. Petraeus started his visit by traveling in a C-130 cargo plane from the capital, Kabul, to the northern province of Kunduz, telling troops with the Army's 1-87, 10th Mountain Division that on this day, there was "no place that [he] would rather be than here" where the "focus of our effort" was.

Northern Afghanistan has seen increased fighting, with the Taliban stepping up attacks as NATO focuses its sights on the movement's southern strongholds. Petraeus was briefed on the situation in the region by German Maj. Gen. Hans-Werner Fritz, the commander of NATO's northern regional command.

In eastern Afghanistan, where NATO forces are trying to prevent insurgents from slipping in from neighboring Pakistan, one U.S. platoon spent Christmas as it does almost every other day - in a firefight with insurgents. Taliban fighters on nearby hills opened fire twice during the day on the platoon's Combat Outpost Badel, sparking short gun battles as the soldiers returned fire. There were no U.S. casualties.

Petraeus also visited the region of one of this year's main NATO offensives in the south, the Taliban stronghold of Marjah in Helmand province, site of some of the heaviest fighting recently with the Taliban.

He praised Marines there for the improvements in the area, which still sees Taliban attacks.

He told the men and women of the Second Battalion, Sixth Marine Unit: "You are part of America's new greatest generation. It is not just the courage that you have shown, it is not just the skills that you have shown in arms. . . . It is the versatility that you demonstrate going outside the wire every day, being ready for a hand grenade or a handshake and knowing what to do if either of those comes your way."

Marjah has become a symbol of the problems facing NATO in Afghanistan. More than 7,000 U.S.-led NATO ground troops launched a nighttime invasion of the region of farming hamlets in February to rout insurgents and cut off their drug-trade income. NATO officials said the effort would pave the way for the Afghan government to move in aid and start delivering public services.

Marine Maj. Gen. Richard Mills declared Dec. 7 that the battle in Marjah was "essentially over." But the campaign took longer than NATO officials had hoped, and illustrated the complexity of trying to wrest control of an area where Taliban influence remained strong.

Efforts to create a civilian government in Marjah have been painfully slow, and U.S. troops struggled against roadside bombs and sniper attacks from an enemy that could blend in with the local population.

Petraeus said "we probably created expectations that were unduly high, and we worked through that."

Still, he said, the progress in Marjah and in other areas helped pave the way for the unanimity achieved at a November NATO summit in Lisbon, Portugal, where member states committed to Afghanistan until 2014.