Secretary of State Colin Powell (search) said Sunday that the United States has a plan to quash the insurgency raging in several Iraqi cities and bring those areas under control in time for national elections in January.

Powell acknowledged that the U.S.-led coalition faces a "difficult time," but he said the Bush administration is committed to making Iraq (search) stable.

"This is not the time to get weak in the knees or faint about it, but to drive on and finish the work that we started," he told NBC's "Meet the Press."

The secretary of state said U.S. commanders are working with Iraqi military leaders and the interim government of Prime Minister Ayad Allawi (search) to put down the extremists in control of Fallujah and other cities.

The insurgency "will be brought under control," Powell said. "It's not an impossible task."

Powell also dismissed the possibility of delaying Iraqi elections, which are scheduled for the end of January. "Nobody's planning to postpone the elections," he said.

"When that insurgency is put down, what the people of the world will see are Iraqis in charge of their own destiny, moving forward toward an election that will provide for a representative form of government," said Powell. "It's going to be something that we'll be able to be proud of.

Later, on "Fox News Sunday," Powell spoke of fighting "a difficult insurgency." But, he added, "We have to make sure that we prevail over that insurgency — not just us, but the Iraqi interim government, as well. And we will prevail. And there will be elections."

Last week, U.S. jets targeted insurgents in Fallujah with missiles over a four-day period. U.S. and Iraqi authorities lost control of the city in April, and Marines turned it over to a U.S.-sanctioned force of Iraqis that has since disappeared.

Powell acknowledged the possibility that the violence could continue in Iraq "for some time. This insurgency isn't going to go away."

He pointed to the buildup of Iraq's security forces and said the Baghdad government increasingly would be able to handle "its own security problem."

"I think the insurgency can be brought down to a level, and I'd like to see it go away entirely. I want to see it defeated. But I think, over time, you will see it being brought under control," Powell said.

The United States realized at the time of the transfer of political control this summer that it was "the time of maximum danger as the insurgents come after us" in hopes of derailing the upcoming elections.

"We're not going to let them go back" to the days of Saddam Hussein (search), Powell said. "We can't let them go back."

"So this is not the time to simply take counsel of our fears and say, 'Oh, this is terrible, terrible.' We've faced challenges like this in the past and we've overcome them, and we'll overcome them in this instance, as well," Powell said.

He added that the United States "did miscalculate the difficulty" of curbing the insurgency after the war, but did not underestimate the challenge being facing now. Thus, Defense Secretary Donald H. Rumsfeld has left more troops in Iraq than the United States had expected to a few months ago.

"When the situation changes, you adjust," Powell said.