The Liwa al-Quds (Jerusalem Brigade) said Abdullah Issa was just a 12-year-old from a poor refugee family who lived in a rebel-held area of Aleppo.
Members of the Nour al-Din al-Zinki Movement are accused of killing him.
It said those responsible were handed over to a judicial committee, and denounced the killing as a "violation".
The US, which has provided military support to the Nour al-Din al-Zinki Movement in the past, said it was seeking more information on what it described as "an appalling report".
"If we can prove that this was indeed what happened and this group was involved... it would give us pause about any assistance or, frankly, any further involvement with this group," state department spokesman Mark Toner told reporters.
Two short videos emerged online on Tuesday morning showing a boy being taunted and then beheaded by a group of Syrian rebels.
The first shows the frightened child, who could be as young as 10, sitting in the back of a pick-up truck, surrounded by five men.
One of the men grips him by the hair as they accuse him of being a member of Liwa al-Quds, a Palestinian militia that fights in support of Syrian President Bashar al-Assad and was involved in clashes with rebels on Tuesday in Handarat, to the north of Aleppo.
The second video shows the boy's murder.
The Syrian Observatory for Human Rights said the boy was seized by rebels in Handarat, but that the killing took place in Mashhad. The UK-based monitoring group could not confirm if the boy was a Palestinian or a child soldier.
Liwa al-Quds issued a statement on Facebook saying that its investigation had found he was a 12-year-old Palestinian named Abdullah Issa, who lived in Mashhad with his family.
It also said he had apparently been receiving medical treatment before being seized, noting that one photograph showed an intravenous drip in his arm.
Liwa al-Quds accused the rebels of killing the child simply because he was Palestinian, in order to take "cheap and despicable revenge" for battlefield losses.
The Nour al-Din al-Zinki Movement said it denounced and condemned "such abuses", but insisted they were "individual errors that represent neither our typical practices nor our general policies".
"All individuals who undertook the violation have been detained and turned over to the [judicial] committee for investigations in accordance with the relevant legal standards," it added.
Earlier this month, Amnesty International published a report detailing a series of violations allegedly committed by Nour al-Din al-Zinki Movement fighters in Aleppo, including abductions and torture.

Mike Brandon, 31, from Bristol, is being treated in Philadelphia after his British consultant said all NHS routes were "exhausted".
Kate Brandon said it had been "by far the hardest three weeks of our lives."
She said her husband had spent the last week in intensive care but was now back on the "wonderful oncology unit".
Mr Brandon was diagnosed with acute lymphoblastic leukaemia two years ago.
In May, his wife raised enough money using a social media campaign to fund his taking part  in "revolutionary" cancer trials at the University of Pennsylvania.
Mrs Brandon said: "We were told that paradoxically the sicker that people become during this treatment, the more likely they are to have a good outcome.
"This knowledge has helped carry us through this excruciatingly difficult time. Boy, did our boy get sick."
Mr Brandon said: "There are plenty of things about a leukaemia diagnosis that are tough: the constant worry about things that may never happen, the strain of the things that have definitely happened, and the stress it places on those closest to me.
"When my leukaemia relapsed in March, we were told that it was time to plan our last days together, but Kate point blank refused. We would fight on, and we have."
A Palestinian boy who was filmed being beheaded by Syrian rebels on Tuesday was not a fighter, a pro-government Palestinian militia has said.
[NEXT_CONCEPT]
A man with a rare type of leukaemia whose wife raised £400,000 to cover his medical costs in the USA is "well under way" with his cancer treatment.