The four-star general, who arrived in the Afghan capital on Friday, faces a tough task to bring peace and secure a face-saving exit for allied troops fighting an increasingly deadly insurgency by the hardline Islamists.
"This is an effort in which we must achieve unity of effort and common purpose. Civilian and military, Afghan and international, we are part of one team with one mission," Petraeus said at the US embassy in Kabul.
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"On this important endeavour, co-operation is not optional," Petraeus added.
Petraeus, who took over as commander of the 140,000 US and NATO troops in Afghanistan after the sacking of US General Stanley McChrystal, has said the war is likely to get tougher before significant improvements are seen.
"This is a tough mission, there is nothing easy about it. But working together we can achieve progress and we can achieve our mutual objective," he told some 1,700 invited guests at a Fourth of July reception.
Petraeus was due to formally assume his commander role on Sunday in a ceremony at NATO's International Security Assistance Force (ISAF) headquarters in central Kabul.
But he has already started on the job, leading Saturday's morning briefing of regional commanders across the country, said ISAF public affairs officer US Air Force Lieutenant Colonel Tadd Sholtis.
"He was actively engaged in asking questions and providing guidance to headquarters personnel and subordinate commands connected to the meeting," Sholtis said.
The general also met Afghan President Hamid Karzai on Saturday, he said, though details of their encounter were not immediately available.
Soldier deaths at record highs
Petraeus arrives as US and NATO soldier deaths are touching record highs in intensified fighting, along with questions about the wisdom of committing such huge resources in manpower and money to what could yet be a lost cause.
His appointment has been welcomed by local officials, including Karzai, who had the support of McChrystal despite frustration in the West over his commitment, particularly towards cracking down on corruption.
Analysts have urged Petraeus to make immediate adjustments to turn around rapidly a war seen as bogged down to the Taliban's advantage.
"A change in the leadership of foreign forces can only be effective if we see more serious steps taken against terrorists," parliamentarian Ahmad Behzad told AFP.
Despite assurances from US President Barack Obama, and Petraeus himself, that change of command does not mean change in strategy, the general has already hinted some tweaks could be in the air.
Troops have complained that McChrystal's "courageous restraint" rule, aimed at minimising civilian casualties, prevents them from properly defending themselves – thus contributing to the spike in casualties.
A total of 102 foreign soldiers died in June, almost triple the May toll and far outstripping the previous highest monthly figure of 77 in August.
So far in 2010, more than 320 troops have died, compared with 520 for 2009, with a British soldier becoming the latest casualty on Thursday.
Petraeus and Karzai
Petraeus's relationship with Karzai - whom Petraeus called on his arrival Friday - would be central to his success, analysts and diplomats said.
Analyst Haroun Mir said he hope that with Petraeus's arrival, the allies could present a united front
"With the arrival of General Petraeus, we hope there will be a unified voice coming from the US administration and also we hope there will be some pressure on President Karzai to fix his government, fight corruption," he said.
"The biggest challenge for David Petraeus is the Afghan government and President Karzai himself -- if the Afghan government does not collaborate, if President Karzai does not own this war then it will be very difficult for General Petraeus to improve the situation."
The scale of the task facing the 57-year-old Petraeus was underscored just hours before he arrived when Taliban militants stormed a US aid organisation, leaving five people dead.
NATO forces also said they accidentally killed two civilians, including a woman, in an overnight operation against Taliban militants in Kandahar.
