Balli said the battle aims to eliminate all remaining IS militants in Baghouz.
The SDF arrested 63 suspected militants in the Syrian city of Raqa Thursday during an operation against jihadist sleeper cells, it said in a statement.
The Islamic State (IS) group is far from defeated, and is morphing into an asymmetrical warfare force after the militant group lost nearly all of the territory it once controlled in Syria, German Chancellor Angela Merkel warned on Friday.
Bali told AFP that around 600 IS fighters are still inside the pocket, a lot of them die-hard foreign fighers.
The enclave, close to the Iraqi border, comprises two villages.
At its height, the jihadist proto-state proclaimed by IS in June 2014 straddled swathes of land in Syria and Iraq and was roughly the size of Britain.
He later wrote on Twitter that the battle had started.
"This battle will be sealed in the coming days", he said.
Among the policy decisions still to be made was what to do about the tens of thousands of Syrian Kurdish fighters that USA forces had trained, armed and advised to carry out the ground war against the Islamic State.
Four years ago, the militants controlled territory the size of Britain and millions of people, but Major General Christopher Ghika, the deputy commander of the U.S. coalition fighting the group, on Thursday said that "now less than one percent of the original caliphate" remains.
Last year, Erdogan threatened to launch a military operation against the Kurdish-majority Syrian region dominated by YPG militia, which Ankara sees as part of the banned separatist PKK movement.
More than 37,000 people, mostly wives and children of jihadi fighters, have fled IS territory since the SDF intensified its offensive in December, according to the Syrian Observatory for Human Rights.
The country's Kurds have largely stayed out of the civil war, instead of developing semi-autonomous institutions in northern and northeastern Syria.
It said US-led coalition's warplanes are giving cover to advancing SDF fighters. According to The Wall Street Journal, the military plans to complete the withdrawal of all U.S. troops from Syria by the end of April. "We have chosen a political agreement with Damascus because we don't want secession from Syria", senior Kurdish official Badran Jia Kurdi told AFP.