Petraeus was chosen to lead US and Nato forces in Afghanistan after General Stanley McChrystal was relieved of his command following a Rolling Stone article in which he and aides were critical of US government officials.
He was previously the head of US Central Command, before being nominated by the US president to lead the forces in Afghanistan.
The approval of the senate committee has cleared the way for a full senate vote on his nomination expected this week, the chairman of the committee said.
The former commander of US forces in Iraq used Tuesday's committee hearing to seek to reassure the senators that he would work closely with his civilian counterparts.
In his testimony, Petraeus warned that it would be years before the Afghan security forces are fully able to take over responsibility in the country.
He said that the task of building up the local police and military, as well as improving local governance was "hugely challenging" in the face of an "industrial strength insurgency", but confirmed an "enduring" US commitment to Afghanistan.
"My sense is that the tough fighting will continue. Indeed, it may get more intense in the next few months," Petraeus told the committee.
Petraeus said that examining the rules of engagement would be one of his first priorities, but that he planned to ensure that the safety of civilians remained a priority.
However, Al Jazeera's Patty Culhane, reporting from Washington DC, noted that the rules of engagement had in fact been signed off by Petraeus in his position at Central Command.
"There have been growing concerns, especially among the military, that the rules of engagement are too restrictive," Culhane said.
"This is a counter-insurgency plan that both McChrystal and Petraeus have been pushing, and the main focus of it was to protect civilians."
"When McChrystal came in and took over in Afghanistan, he said that too many civilians were being caught up in the cross-fire and he severely restricted things."
But Hillary Mann Leverett, a former US official on Afghanistan and member of the Council on Foreign Relations, told Al Jazeera that the resultant changes did not yield intended results.
"The reality is that there has not been a decrease in civilian deaths with the rules of engagement that was adopted by McChrystal," Leverett said.
"If General Petraeus does adopt looser rules of engagement, that would potentially lead to more civilian deaths. We are then likely to see even more violence, particularly more suicide bombings targeted at US forces and Nato troops."
Despite the warnings and the possibility of "tweaks" to the rules of engagement, he made it clear that he supported Obama's underlying strategy, including the goal of beginning a transition of authority to Afghan forces and a gradual reduction in US troops starting in July 2011.