General Stanley McChrystal says the crucial operation will carry into the fall, instead of wrapping up before the Muslim holy month of Ramadan in August.
McChrystal says the process of gaining local support is taking longer than planned, and he doesn't want to "rush it."
Kandahar is Afghanistan's second-largest city and the birthplace of the Taliban insurgency. The NATO-led military force in Kandahar will roughly triple by this summer.
A Taliban commander in the province told CBS News on Thursday that aat a wedding party in Kandahar was "collective punishment" for villagers who had established their own non-Taliban defenses.
The family targeted in the attack includes at least three Afghan national police officers.
Meanwhile, a local government official in neighboring Helmand province tells CBS News that Taliban militants hanged a seven-year-old boy earlier this week after accusing him of spying for international forces.
Afghan President Hamid Karzai said that if the hanging was proven, it would be a "heart breaking and shocking" occurrence.