An Italian fighting alongside a Kurdish-led force to expel the Islamic State group from its last pocket of territory in eastern Syria has been killed, the force said Tuesday.

Lorenzo Orsetti, 33, was killed in battle on Sunday as he fought diehard jihadists in the village of Baghouz, a spokesman for the US-backed Syrian Democratic Forces said.

"Two days ago... he was at the forefront of the fighting and he died in battle," Mustefa Bali told AFP.

"He was a frontline fighter in the ranks of the People's Protection Units" or YPG, a Kurdish force spearheading the SDF, he said.

"He participated in more than one battle and more than one SDF campaign" against IS, Bali said.

Orsetti even fought to defend the Kurdish enclave of Afrin in northwest Syria, before it was overrun by Turkish-backed Syrian rebels a year ago, he said.

IS published a photograph of the slain fighter and a snapshot of his healthcare card on its social media channels Monday, claiming to have killed him in Baghouz.

The YPG on Tuesday released a video of Orsetti, in which the Italian said he joined the Kurdish force of his own free will, knew the risks involved, and had no regrets.

Dressed in military uniform and with a weapon in his hand, he said he was in Syria mainly "because I believe in freedom -- I'm an Anarchist -- and I was tired of my life in... Western society".

- 'I love you all' -

"If you see this message, probably something's going... you know," he said, a yellow triangular-shaped YPG flag on the wall behind him.

"I love you all, all of you -- all of you (who) passed through my life: my friends, my family -- my dog," he said.

"Long live Kurdistan, long live the YPG and the YPJ," its female fighter units, he added in Kurdish.

Orsetti's father told Italian newspaper Corriere della Sera he and his wife were "very proud" of their son.

A former waiter and chef from Florence, Orsetti had initially travelled to Syria in September 2017 as an observer but felt "increasingly involved", his father said.

His body "is apparently still in a combat zone. We hope to be able to recover it as quickly as possible," he said.

"Lorenzo once told us he'd love to be buried in Syria. We don't know what we'll do yet, but I think we'll respect his wishes".

Orsetti had left a "last testament" cited by La Stampa daily and other media.

"I have no regrets. I died doing what I believed was right, defending the weak," it read.

According to the Corriere della Sera, some 25 Italians have travelled to Syria since 2015 to fight alongside Kurdish forces.

Three men and two women are still there, it said.