"As you increase your tempo and expand your area of operations. That, indeed, violence goes up. And violence going up means that casualties go up, as well," Petraeus said.
But he said progress was being made and the Taliban's momentum was reversed in "some areas", citing Marja -- the focus the first major operation implemented by Gen. Stanley McChrystal as surge troops were coming in.
"I think there's no question that in Helmand Province, the six central districts of Helmand Province-- are a good bit more secure than they were even six months ago," he said.
"Marja -- as hard fought and as embattled as it has been, three days ago opened up its high school for the first time in six years. Three other schools will open for students ... . It has an interim police station. The market is no longer a market in which the narcotics industry puts its wares on sale."
"Very hard fought gains," he continued. "Very difficult and sometimes seeming to be as slow as watching grass grow or paint dry."
He admitted there were still challenges in those areas.
"Our troopers are still fighting, we're still taking casualties in those areas, because the enemy fights back when you take away really significant sanctuaries and safe havens," he said.
"What we intend to do over the course of the months that lie ahead is to expand the security bubbles in various areas. In some areas, we have already reversed the momentum of the Taliban. In others, we still need to do that and we are intent on doing that."
Petraeus acknowledged there was still much more work to be done on other elements of the war, not just with security.
Of the effort to reintegrate anti-government insurgents into Afghan society in exchange for pledging to renounce al-Qaeda, putting down arms against the government, and abiding by the Afghan constitution, Petraeus said so far, only "small numbers" have come in to do so.
"But we do see the beginnings of it. And, of course, the formal program, the Afghan-led reintegration of reconcilables, that program is really just beginning to roll out now."
Soon, he said, Karzai would announce the membership of the national peace council created during June's peace jirga to reconcile with senior members of the Taliban and other anti-government insurgents.
"That will be another important step in this process," he said.
Another important piece of the process is dealing with Afghan government corruption, which 95 percent of Afghans cited as a problem in an ABC News poll conducted last winter. Widespread belief that the Afghan government is corrupt not only undermines the credibility of the central government, but the attempt to win the hearts and minds of Afghans.
Petraeus said Afghan President Hamid Karzai's government has taken a number of actions against corruption, including after news that the Central Bank had removed Kabul Bank's chairman and CEO after it was found that tens of millions of dollars had been funneled into risky Dubai property investments, and loans were given to shareholders with close links to the Karzai Administration.
"In recent years, indeed even in recent months, various elements of President Karzai's government have taken a number of actions against corruption," Petraeus said.