The Syrian Democratic Forces (SDF) "started to move on to the last village remaining under jihadists' control in [northern] Syria", said SDF press officer Mustafa Bali on Saturday evening.
An SDF statement said the offensive was focused on the village of Baghouz.
Over the last four years of the anti-ISIS fight the U.S. has invested in some infrastructure in eastern Syria, including some small bases, observation points and airstrips. "We have launched an assault and the fighters are advancing", an SDF field commander told AFP Sunday.
"I suggested to my U.S. counterpart, Mike Pompeo, the idea of establishing a joint task force to coordinate the U.S. withdrawal from Syria, and he agreed to my proposal", said the minister.
With many foreign governments reluctant to repatriate citizens who supported ISIS, and Syria's Kurds insisting they are unable to hold the prisoners long term, rights organisations have warned that foreign fighters face illegal rendition to Iraq.
US and SDF officials say, however, they have no reason to believe he is there. Since 2011, Syria has been embroiled in a violent civil war, which created a safe haven for extremists and allowed ISIS to spread quickly.
President Donald Trump, who is planning to pull US 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.
The airstrike is the latest in a string bombings targeting the last IS redoubt in the eastern Euphrates River region.
Backed by air raids by the US-led coalition against ISIL, the Kurdish-Arab alliance has in recent months cornered the remaining ISIL fighters in a final patch of territory in the eastern province of Deir Az Zor.
It said the USA -led coalition struck positions of the IS in the eastern Euphrates to practice more pressure on the group.
Success against the Islamic State in Baghouz would also increase pressure on the USA military to pull out of Syria, in accordance with Trump's instructions that the troops should leave once the Islamic State has been defeated.
In that time, more than 1,200 IS militants, more than 670 SDF fighters, and around 400 civilians have been killed in the fighting, the Observatory says. Human Rights Watch knows of at least five foreign detainees who were handed to Iraq's Counter Terrorism Service by United States forces after being captured in Syria, according to the group's Iraq researcher Belkis Wille.