He said Taliban resistance had been "a bit disjointed" but "formidable".
"The way the operation was conducted leaped over some of them. But there is tough fighting going on without question," he said.
Petraeus said the campaign, which started on February 13, would not stop with Marjah and nearby Nad Ali.
"This is just the initial operation of what will be a 12 to 18-month campaign as General [Stanley] McChrystal [the head of US and Nato forces in Afghanistan] and his team mapped it out," he said.
Barack Obama, the US president, ordered 30,000 more US troops to Afghanistan last year in a plan he said that would enable American soldiers to begin pulling out as early as July 2011.
The stated aim of the Nato-Afghan offensive in Marjah is to bring government control over the region with security, clinics and schools planned for after the Taliban has been subdued.
But more than a week into the campaign, fears of a humanitarian disaster are mounting.
Aid groups say they are worried many Marjah residents remain trapped, and that for those displaced, they will not have enough supplies to help them.
"People who are ill cannot get to hospitals and others cannot bring them medicines," Ajmal Samadi, the head of the Afghan Rights Monitor group, said.
"They cannot get food or even go outside to look after their farms."
The Marjah operation is a major test of a new US and Nato strategy that stresses protecting civilians over routing Taliban fighters as quickly as possible.
Eric Tremblay, a spokesman for Nato-led troops in Afghanistan, told Al Jazeera on Sunday that coalition forces had made civilians' safety their priority.
"General Stanley McChrystal has made it quite clear to our coalition partners and the Afghan national security forces that ... the strategy is to protect the population; it is about separating the insurgency from the population," he told Al Jazeera from Kabul on Sunday.
Despite Nato assurances, Hamid Karzai, the Afghan president, again called on international troops to prevent civilian deaths.
Addressing parliament's opening session in Kabul on Saturday, he said: "We need to reach the point where there are no civilian casualties. Our effort and our criticism will continue until we reach that goal."
Haji Zahir the newly appointed district governor of Marjah, said he would visit the town on Monday to discuss security and reconstruction with community leaders.
But questions remain about what happens after the military operation and whether Afghan forces can handle the rebuilding and security operations with Nato forces.
Speaking to Al Jazeera, Colin Powell, the former US secretary of state and chairman of the joint chiefs of staff, said the "real test" would be for the Afghan national police.
"They're the ones who will keep security in the region after the armies have moved out of the way. Armies fight people. Police protect people over the long-term and that I think is the real challenge in Afghanistan," he said.