The Syrian Democratic Forces (SDF), supported by a US-led coalition, announced a final push to retake the jihadist pocket near the Iraqi border late Saturday, after a pause of more than a week to allow civilians to flee.
The Syrian Observatory for Human Rights reported heavy clashes between both sides on Sunday morning, as coalition planes and artillery bombarded jihadist positions.
"The battle is ongoing. There were heavy clashes this morning, with landmines going off," said Rami Abdel Rahman, the head of the Britain-based war monitor.
The SDF launched an offensive to expel IS from the eastern province of Deir Ezzor in September.
The Kurdish-led alliance has since whittled down jihadist-held territory to a patch of just four square kilometres (one square mile) on the eastern banks of the Euphrates.
Up to 600 jihadists could still remain inside, most of them foreigners, according to SDF spokesman Mustafa Bali.
Since fighting intensified in December, more than 37,000 people, mostly wives and children of jihadist fighters, have fled out into SDF-held desert areas, the Observatory says.
That figure includes some 3,200 suspected jihadists detained by the SDF, according to the monitor, which relies on sources inside Syria for its information.
But separate military offensives in both countries, including by the SDF, have since retaken the vast bulk of the cross-border "caliphate" they declared in 2014.