The city's worsening security has prompted the United Nations to shut its Kandahar office and withdraw foreign staff from the city.
"There have been tough moments here in Kandahar in recent weeks - that is well known - and we know that there will be more tough moments in the weeks and months ahead," Petraeus said.
"As we learned in Iraq, and as we have re-learned in Afghanistan, when you fight to take away the momentum and the sanctuaries and the safe havens of the enemy, the enemy fights back. And that can be difficult and tough to fight."
As a result, Petraeus said, the security situation was likely to get worse before it gets better.
"The enemy is going to take horrific actions to disrupt the progress that Afghan and coalition civilian and military elements are working so hard to achieve," he said.
The US build-up around Kandahar is a key part of the additional deployment of 30,000 troops ordered by Barack Obama, the US president, in an effort to turn the tide in the Afghan war, now into its ninth year.
|US forces are massing for a major offensive against the Taliban [Reuters]
By August there will be around 100,000 US troops deployed in Afghanistan, more than three times as many as when Obama took power.
US commanders have said the Kandahar operation will be one of the last to take advantage of that surge in troop strength.
Thousands of additional US troops have already entered rural districts of Kandahar since the middle of last year and while Petraeus said they had made gains, he acknowledged that several areas remain under Taliban control.
"The shaping operations, the preparatory operations have been ongoing already for some months," Petraeus said, adding that as the new forces arrive, "the intensity of
security operations will increase accordingly".
"The operation in Kandahar is not going to be a conventional offensive," he said.
"The enemy fights back, and our experience in Iraq was that it got harder before it got easier."