The U.S. -backed fighters on Saturday launched a final push to clear the area from IS.
"The SDF has launched its final battle to eliminate the terrorist ISIS organization in Al-Baghouz village; the last ISIS stronghold", the SDF said, using an alternate abbreviation for the terror group.
Gen. Christopher Ghika, deputy commander-strategy and information for the US-led coalition, said Islamic State fighters "are attempting to escape through intermixing with the innocent women and children attempting to flee the fighting".
Some 600 people were able to reach SDF territory on Sunday after fleeing the fighting, the Observatory said.
The fighting is expected to be over within days, Mr Bali said.
The SDF, backed by the US-led coalition, has defeated ISIS across a swathe of northern and eastern Syria in recent months, reducing its once expansive caliphate to a fraction of its peak size.
France's Defence Minister Florence Parly visited the Iraqi side of the border on Saturday where France has a forward artillery base near al-Qaim, just a few kilometres from Baghouz.
"We are going to have to continue to put military pressure on them".
Trump is moving ahead with his plan to withdraw 2,000 US troops from Syria, despite warnings from USA military and security experts that militants in Iraq and Syria could prepare an insurgency if USA -led forces back off.
The US is "on track" to withdraw from Syria, US Army General Joseph Votel said Sunday.
Bali told AFP that around 600 IS fighters are still inside the pocket, majority die-hard foreign fighers.
The source said both Turkey and the US agreed that the process has gathered momentum.
Despite Trump's decision, America still has 2,000 or so troops in Syria.
"At this point it doesn't really matter what they say because, we know where they are".
IS overran large parts of the country and neighboring Iraq in 2014, declaring a "caliphate" there, but various military offensives have reduced it to a fragment.
As the SDF closed in, there were reports that two Canadian women and their children who had been living in the ISIS-controlled area had surrendered to the USA -backed forces, CNN and CBC reported Sunday.
Syria's war has killed more than 360,000 people and displaced millions since it erupted in 2011 with the brutal repression of anti-government protests.
The YPG has spearheaded the SDF, the US' main ally in Syria.
A United Nations report seen by Reuters last week estimated there are up to 18,000 ISIS terrorists in Iraq and Syria, including up to 3,000 foreign fighters. "They have had the opportunity to prepare this for a while, and there is a presence of civilians in the area - family members of ISIS and then others that reside in the area, so I think this poses a significant, a significant concern for us as we do this", Votel said.
In recent weeks, US 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.