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JANE ARRAF, CNN CORRESPONDENT embedded with troops near Falluja.

CALLAWAY: On the phone with us now, we have CNN's Jane Arraf, who is embedded with troops near Falluja.

Jane -- good morning to you.

And what is the situation there?

JANE ARRAF, CNN CORRESPONDENT: Good morning.

The situation is they're closing in on what military commanders believe might be the last pockets of organized insurgents. Now, that doesn't mean there aren't more insurgents out there. There are, and they keep popping up. But here in the southeast corner of town, they have been dropping 500 pound laser guided bombs on a series of spider holes, hiding places of insurgents that they've been finding.

They've also been finding tunnels, bunkers, landmines, homemade bombs and a variety of defensive positions and defensive strategies as they move through these streets. So far in the last couple of hours, they believe that they have killed about 20 suspected insurgents in the latest fight and they say they believe that this is where insurgents have been channeled from other parts of the city. This is, perhaps, the last stand, they hope, of organized insurgents.

CALLAWAY: Jane, we're hearing numbers from 600 to 1,000 insurgents who have been killed in this battle.

What are you hearing from the field there?

ARRAF: That would fit. We're with an Army unit that is essentially paving the way with its heavy armor and other assets for infantrymen from the Marines and other units to follow. They have been, their casualty count has been quite high. They've been using a variety of things, as I've mentioned. When you drop a laser guided bomb on a bunker, you're bound to kill quite a lot of people. So they have actually been keeping quite a high, relatively high count.

We have to point out that we are in an area of town which has been an insurgent stronghold. Here it is thought to be a particular stronghold of the Zarqawi network. And it has long ago been cleared of civilians. Not a single civilian in sight in this part of town.

CALLAWAY: Do the troops feel as if they've turned a corner yet in this operation into taking full control of Falluja?

ARRAF: Not full control. Certainly they believe they have control of most of it and that they're rapidly continuing to take control of the remaining parts. Full control in the sense that they have control of major sectors. But what they still have to do and what they will continue to do for some time to come is that street by street, building by building process.

Now, they've been doing some of that here, the Army unit task force from the 1st Infantry Division. And we were taken into a house earlier this morning where they had found a vehicle mounted with a machine gun, rocket propelled grenades. As we walked into the house, there were two suspected gunmen lying on the floor.

CALLAWAY: Wow!

ARRAF: That's the kind of thing they've been doing, going house to house.

CALLAWAY: All right, Jane Arraf somewhere near Falluja.

Thank you, Jane, for that report.