McChrystal is expected to conduct a review of military strategy and make recommendations on any changes within two months, the Pentagon said.
The general said it would be a critical year for the coalition in Afghanistan.
He warned while Nato forces are “operating with care, we will not be timid.”
This was a reference to increasing criticism of the heavy civilian casualties sustained in the US’ battle against the Taliban.
Hamid Karzai, the Afghan president, reminded McChrystal of the military’s obligation to protect civilians during talks at his palace on Sunday.
“The most important element of the mission of the new Nato/coalition forces commander in Afghanistan is to protect the civilian population during the anti-terrorism military operations,” Karzai told the general.
McChrystal said Nato forces would “win the support of the Afghan people” through “intelligence-driven precision operations, subordinate to efforts protecting development projects and Afghanistan’s population.”
General David McKiernan, McChrystal’s predecessor, was removed from his position as the US military was accused of killing scores of civilians in an anti-Taliban operation.
US war planes targeting Taliban positions in the southwestern province of Farah on May 4 struck compounds where locals said villagers had taken shelter from heavy fighting between the army and Taliban fighters.
The Afghan government said 140 civilians were killed. Though the US military admitted civilian casualties, it maintained only 20-30 civilians were killed.
Thousands of mostly US troops are arriving in the country to ensure the presidential election, scheduled for August, goes smoothly, and to reinforce the south of the
country, a Taliban stronghold.
There are about 56,000 US troops in Afghanistan, making up most of the nearly 90,000 international forces assisting in the battle against the Taliban.