Rockets pounded Baghouz overnight on Monday (March 12), the Syrian village that represents Islamic State's last territory in Syria.
A spokesman for the Syrian Democratic Forces said the U.S.-backed offensive is as good as over and at least 38 IS fighters were killed.
The SDF has been laying siege to the village for weeks, making modest advances against sniper fire and landmines.
The final assault was postponed to allow the evacuation of thousands of civilians, the bulk of whom have been transported to a camp in the northeast.
There they face dire conditions.
Reuters' Ellen Francis visited one.
(SOUNDBITE) (English), REUTERS REPORTER ELLEN FRANCIS, SAYING: "The camps for the displaced in northeast Syria have long been overcrowded with families.
But now it's getting worse.
Thousands more people have arrived this week (...) Camp workers said they don't have enough tents or food as children arrive barefoot and hungry." While it was designed to accomodate 20,000 people, the UN says the camp is sheltering up to 66,000.
Many of them are the wives and children of Islamic State fighters.
(SOUNDBITE) (English), REUTERS REPORTER ELLEN FRANCIS, SAYING: "Nobody expected such a huge influx of people.
It's a bit calmer here than another camp.
We visited a few days ago which was already overflowing with Syrians and Iraqis who fled their homes." While the defeat of Baghouz will mark a milestone in the campaign against Islamic State, Washington does not believe any senior leaders are in the village.
The jihadist group is shifting its strategy into underground cells and also still operates in more remote areas.