SDF spokesman Mustafa Bali said on Twitter Sunday that its forces were engaged in "direct violent clashes" and that its planes were targeting weapons depots.
The battle opened on Sunday evening with large explosions and mushroom clouds rising into the air over Baghouz, on the Euphrates River in eastern Syria, as the Syrian Democratic Forces battered the village with artillery and gunfire, hitting an ISIS ammunition dump.
A senior USA defence official said last week that the SDF is believed to have about 5,000 IS fighters in captivity, of whom about 4,000 are Iraqis and Syrians.
The SDF said Sunday it had started an attack to capture Daesh's last remaining shred of territory in eastern Syria after the terror group failed to meet a deadline to surrender.
The AP viewed it from a house captured by the SDF that Isis appeared to have used as a clinic by Isis.
Abdel Rahman said that, so far, some 20,000 people, including 2,400 Islamic State fighters, have handed themselves in to SDF in the past two weeks. After intense air and artillery strikes on 1 March, the alliance said it had to slow down the offensive "due to a small number of civilians held as human shields".
The battle to retake Baghouz has been ongoing for the past few weeks but has often been halted to allow for the evacuation of civilians.
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"Our forces will pause the offensive if we see more civilians who wish to evacuate the area or if we need to free any hostages", Efrin stated.
Since December, almost 59,000 people have left the last IS redoubt, according to the Syrian Observatory for Human Rights, around a tenth of them suspected jihadist fighters.
Fires raged after dark in the enclave at Baghouz near the Iraqi border as it was targeted with rockets and thick plumes of smoke rose from the area, Reuters TV footage showed.
At the height of its brutal rule, IS controlled a stretch of land in Syria and Iraq the size of Britain.
"The operation will continue until Baghouz is liberated and until the end of the terrorist military presence in that area", he added.
Aid agencies are struggling to cope with the thousands of weak and hungry people who have fled Baghouz. At least 100 people, mostly children, died en route to al-Hol or shortly after arriving due to a combination of malnutrition and hypothermia.
12,000 came out of Baghouz to one camp in just a 48 hour span last week, and some of the civilians at the camp say that there are as many left in Baghouz as have left, all underground, pouring out in numbers.
"The message that these children are not wanted is growing stronger and stronger", said Geert Cappelaere, UNICEF's Middle East director.