Bali told Reuters in the last 10 days SDF fighters had handled the battle "patiently" as more than 20,000 civilians were evacuated from the besieged enclave.
"It should be formally announced sometime, probably next week, that we will have 100 per cent of the caliphate", Trump told representatives of the 79-member, USA -led coalition fighting IS.
SDF spokesman Mustafa Bali said: "The battle has started". But after almost two weeks of waiting "patiently", they are now due to begin their offensive on the final ISIS territory - which comprises of just two villages near the Iraqi border.
He later postponed the operation after talks with his American counterpart Donald Trump, who announced a U.S. troop pull-out from Syria.
Trump wants to withdraw US troops from Syria by the end of April, a plan that has alarmed European allies including Germany.
A large presence of American troops remain in Syria, but local forces fear what comes next if the USA completely pulls out.
Special Operations forces working alongside the SDF fighters will be particularly keen on establishing whether any key Islamic State leaders are still holed up in Baghouz, including perhaps the Islamic State's leader, Abu Bakr al-Baghdadi. U.S.
Speaking at the State Department on Wednesday, February 6, Trump said that US-led troops and their Kurdish allies should formally announce the end of the "caliphate" some time next week.
The SDF, backed by air strikes carried out of the US-led coalition, has driven out IS from towns and villages in north-eastern Syria in recent months.
The jihadists are now clinging on to a small sliver of land near the village of Baghouz in eastern Syria and many residents are fleeing and turning themselves in ahead of a final offensive. "This was the foreign fighter element, some of his most trusted people".
The Britain-based war monitor has said that figure includes some 3,200 suspected militants.
The U.S. military presence in Syria has offered the Kurds a measure of protection against any Turkish offensive.