The approval of his nomination by the Senate Armed Services Committee sets up a vote by the full Senate.
Petraeus told senators he would insist on "an unshakable commitment to teamwork among all elements of the U.S. government," The Washington Post reported.
"We are all firmly united in seeking to forge unity of effort," Petreaus said.
Petraeus used his opening statement before the panel to praise his predecessor, Gen. Stanley McChrystal, fired by President Barack Obama for disparaging comments he made in a Rolling Stone magazine article.
Petraeus received bipartisan praise from members of the panel. Sen. John McCain, R-Ariz., called Petraeus an "American hero" for his performance in the Iraq war, the Post said.
Petraeus said U.S. and NATO troops would go after the enemy while taking steps to protect civilians.
"Our forces have been doing that, and we will continue to do that," he said. "I am keenly aware of concerns by some of our troopers on the ground about the application of our rules of engagement and the tactical directive. They should know that I will look very hard at this issue."
Petraeus was questioned about whether he backs Obama's policy to start pulling U.S. troops out of Afghanistan in July 2011, depending on the situation at the time.
"Not only did I say I supported it, I said I agreed with it," Petraeus said.
The drawdown deadline, Petraeus said, "was not just for domestic political purposes. It was also meant for audiences in Kabul, that we will not be there forever. But we will be there, presumably for quite some time."
Sen. Lindsey Graham, R-S.C., complained about what he said is a lack of unity about what will happen in July 2011.
"Somebody needs to get it straight, without a doubt, what the hell we're going to do in July," he said.
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