Three Syrian Democratic Forces (SDF) fighters were also killed in the battle, Mustafa Bali, the head of the SDF media office, said in a post on Twitter.
The members of the SDF moved towards a tent encampment in the village of Baghouz and at one point encircled a group of ISIL fighters, killing a number of them in an hour-long battle, Bali said.
Al Jazeera's Hoda Abdel-Hamid said the fighting was the "heaviest yet" in the battle to retake Baghouz.
"Coalition forces have carried out about 30 air strikes hitting defence positions but also weapon storage facilities," she said, speaking from the Turkish border town of Gaziantep.
"Most of the shelling and bombing happens under cover of darkness, and then in the morning there is a sort of standoff situation where the Kurdish forces on the ground wait to see if there is any kind of reaction coming from the ISIL leadership that is still inside Baghouz," she continued.
After weeks of besieging Baghouz, the operation launched on Sunday night aimed at finally taking the last tiny patch of land held by ISIL, a pocket on the banks of the Euphrates River in eastern Syria near the border with Iraq.
The operation against ISIL "will continue until we totally wipe them out", the SDF vowed in a statement on Monday, saying they had made "tangible progress".
The US-led coalition has been surprised by the "resilience of the ISIL fighters" in Baghouz, Abdel-Hamid said.
About 500 ISIL fighters are believed to be holed up in the territory, along with possibly 3,000 to 4,000 civilians, including women and children - mainly family members who remained after thousands of civilians streamed out of Baghouz in the past weeks during pauses in the fighting.
The fighters are heavily dug in and have planted landmines and booby traps in the area.
The capture of Baghouz would be a milestone in the devastating four-year campaign to defeat the group's so-called "caliphate" that once covered a vast territory straddling both Syria and Iraq.