"The stakes are very high," he said at a Baghdad ceremony, as he took command of about 130,000 US troops in Iraq.
Petraeus, a veteran of two tours of Iraq and a counter-insurgency expert, has called for the additional American troops to be deployed as quickly as possible.
"The rucksack of responsibility is very heavy ... we will all have to share the burden and move forward together," Petraeus told his audience at Camp Victory, a US base on the outskirts of the capital.
During his time as commander of the US 101st Airborne Division in 2003, he won plaudits for working closely with local leaders to improve security in the northern city of Mosul.
He also led the effort to train Iraqi security forces and his counter-insurgency manual emphasises the importance of understanding local politics and culture, two things which could be vital in achieving success.
Some Iraqis have said one of the most positive developments of the new strategy is al-Maliki's commitment to target both Sunni and Shia fighters.
Hoda Abdel Hamid, Al Jazeera's correspondent in Baghdad, said: "Many Iraqi officials ... pointed out that the most important thing could be the new attitude of al-Maliki who has convinced Sunni leaders ... he is extremely serious about going after anyone who is holding a weapon outside the law."
Petraeus, who has a doctorate in international relations, took over the command from US general George Casey.
Ahead of the ceremony, the outgoing commander said: "My greatest fear is that the Iraqis can't put the past behind them.
"We liberated them from 35 years of tyranny. We can't liberate them from the fears and prejdices that grew up in that 35 years. They have to do that themselves," Casey said.
More than 3,000 US soldiers and tens of thousands of Iraqis have died since the the invasion in 2003 and support for a continuing US presence among American voters is at an all-time low, despite Bush's new strategy.