Meanwhile, US-backed Syrian forces awaited orders Sunday to relaunch their push against the Islamic State group's final scrap of territory as an earlier exodus of civilians from the redoubt slowed to a trickle.
Gen. Joseph Votel, the top USA general overseeing military operations in the Middle East, also warned Thursday that the fight against ISIS is "far from over" despite the terror group's territorial losses and cautioned that the remnants of the group are positioning themselves for a potential resurgence.
However, the USA does not believe any senior Islamic State leaders are in Baghouz, assessing they have gone elsewhere as part of the group's shift towards guerrilla tactics, a U.S. defence official said.
At its height, ISIS controlled huge swaths of territory in Syria and Iraq.
Amid the rubble, three SDF fighters lobbed a salvo of mortar shells towards the IS pocket, hours after the first attempted counterattack at daybreak under the cover of a dust storm.
"Number of Daesh members surrendered to us since yesterday evening has risen to 3,000", Kurdish spokesman Mustefa Bali tweeted Tuesday evening.
Gen. Joseph Votel, the top USA general overseeing military operations in the Middle East, told the House Armed Services Committee last week the fight against ISIS is "far from over" despite their losses in territory.
Around 3,000 Islamic State members have surrendered from the group's last holdout in Syria, Kurdish-led forces said Tuesday, as air raids and shelling resumed after a brief lull.
But an SDF official said on Wednesday that "it appears as though many fighters remain inside" Baghouz.
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.
Islamic State's defenses include extensive tunnels.
SDF commander Adnan Afrin said many jihadist fighters had been killed or wounded since the assault began on Sunday.
Fighters surrendering from Baghouz are questioned and searched.
The SDF has shipped most people fleeing the wreckage of Daesh's rule over recent weeks to al-Hol in northeast Syria where some 65,000 people now live in a camp that the United Nations says was built to house 20,000.
"If we had thousands of kilometres and now we only have some kilometres left, it is said we have lost, but God's judging standard is different", said a man named Abu Abdel Adheem, in the video published via IS social media channels. The World Health Organization said on Tuesday that 106 people, mainly infants, have died since December on the journey to Al Hol, which takes at least six hours. Many evacuees, particularly foreigners, still express obdurate support for Islamic State, posing hard security, legal and moral questions for their countries of origin.
Obdurate support voiced by many evacuees for ISIS, particularly among foreigners, has posed a complex security, legal and moral challenge. Britain stripped her of her citizenship on security grounds last month.