Senior military commanders told FOX News that they are considering a slight increase in combat power in Iraq prior to that country's elections at the end of January.

The Washington Post, citing unnamed military commanders, reported on Monday that the top brass is considering increasing the total number of combat forces to go after terrorists that fled Fallujah after the U.S. and Iraqi-led offensive there.

Click here to read The Washington Post story.

U.S. and Iraqi troops continue to clear the last of the resistance from Fallujah, the main rebel bastion that was stormed Nov. 8 in hopes of breaking the back of the insurgency before the Jan. 30 election. American commanders said U.S. and Iraqi forces killed more than 1,000 enemy fighters during the eight-day battle there and found torture chambers and the suspected headquarters of Al Qaeda-linked terrorist Abu Musab al-Zarqawi (search).

The Pentagon last month ordered about 6,500 soldiers in Iraq to extend their tours by up to two months. Military officers told the Post that the exact number of extra troops needed is still being reviewed but estimated it at the equivalent of several battalions, or about 3,000 to 5,000 soldiers. The number of U.S. troops in Iraq fell to nearly 100,000 last spring before rising to 138,000, where it has stayed since the summer.

Senior commanders told FOX News that the increase being considered in Iraq will be much like the increase seen in Afghanistan prior to those elections, but on a bigger scale.

The troop movement in Iraq has always been a possibility, and now with the success in stomping out much of the insurgency in Fallujah (search), one senior commander said: "We have to keep the pressure on."

Lt. Gen. Lance Smith, deputy commander of U.S. Central Command (search), said Friday that military leaders will further assess the situation as time goes on and will look at the impact of the Fallujah operation on the entire country. Currently, the United States has 18 brigades in Iraq.

"We will expect, by using extensions of some troops that were only planning on being over there for 10 months, extending them another two months so that they still would be on the ground, you know, about a year, and using that to add additional forces over there," Smith said. "The issue, by the way, is not just numbers. The issue is really about experienced troops during this period of time of expected increased violence."

Smith postulated that about an additional brigade's worth of forces may be needed but that number hasn't yet been finalized. It's not the military's intent to keep troops in Iraq beyond a year, Smith said. A brigade is usually 2,500 to 3,500 troops.

"If we believe the security situation requires that, we will make the appropriate recommendation to the secretary and through our leadership channels," he added.

Troop numbers could reach about 141,000 to 145,000, Smith said.

The military also hasn't ruled out using the U.S. strategic reserve forces, he said.

"But again, I think too early to try and decide that until we really see what's happening with the — after — in the aftermath of Fallujah."

FOX News' Bret Baier and Ian McCaleb contributed to this report.