The Syrian Democratic Forces (SDF), supported by a US -led coalition, announced a final push to retake the militant pocket late Saturday, after a pause of more than a week to allow civilians to flee.
Mustafa Bali, the head of the SDF media office, told Reuters the aim of the assault was to "eliminate the last remnants of the terrorist organisation" and called it the "last battle".
Up to 600 militants could still be inside, a lot of them foreigners, said SDF spokesman Mustafa Bali.
Some 600 people were able to reach SDF territory on Sunday after fleeing the fighting, the Observatory said.
The statement gave no indication of how long it could take to capture Baghouz, but President Donald Trump said last week he had been told that the full territorial conquest of the Islamic State could be completed in the coming week.
Backed by coalition air strikes, the SDF alliance has been battling to oust the jihadists from the eastern province of Deir Ezzor since September.
The surprise announcement prompted the U.S. military to caution in a report published this month that the group "could likely resurge in Syria within six to 12 months and regain limited territory" if sustained pressure is not maintained.
President Donald Trump, who is planning to pull USA forces out of Syria, said on Wednesday he expected a formal announcement as early as this week that the coalition had reclaimed all the territory previously held by ISIL.
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A senior military official from the SDF said that other members of IS's foreign legion had joined the fight against Baghdadi, including some Algerians and Moroccans.
Bali said there were "dozens of SDF hostages" captured by ISIL.
He has also mentioned that Moscow has not seen progress in the United States implementing its decision to withdraw troops from Syria.
IS overran large parts of Syria and neighbouring Iraq in 2014, declaring a "caliphate" in areas it controlled.
"The coalition's hard-won battlefield gains can only be secured by maintaining a vigilant offensive against the now-largely dispersed and disaggregated ISIS that retains leaders, fighters, facilitators, resources and the profane ideology that fuels their efforts", Votel added. But activists and residents say IS still has sleeper cells in Syria and Iraq, and is laying the groundwork for an insurgency.
Hundreds of civilians are also believed to be inside.
The group says it is aware of at least five foreign ISIS suspects who were transferred from Syria to Iraq by USA forces.
In recent weeks, USA officials have said IS has lost 99.5 percent of its territory and is holding on to under 5 square kilometers (under 2 square miles), where most of the fighters are concentrated in Syria. It has sent vehicles into eastern Syria as well as artillery.