The image of shell-shocked five-year-old Omran Daqneesh sitting alone in an ambulance, covered in dust and blood, shocked the world and inspired Alex, from Scarsdale, New York, to write a 3-page letter to Obama.
In a handwritten letter sent to the White House, Alex asked Obama to go and collect Omran and bring him to his house where "we will be waiting for you guys with flags, flowers, and balloons."
Obama read Alex's words aloud in a speech he gave at the United Nations earlier this week, before posting a video of Alex reading the letter himself to Facebook.
In his message, Obama asked people to read the letter to "understand why he had decided to share it with the world."
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"Those are the words of a six-year-old boy -- a young child who has not learned to be cynical, or suspicious, or fearful of other people because of where they come from, how they look, or how they pray," the President wrote.
The post has collected more than 100,000 "likes" and been shared more than 60,000 times, with many Facebook users praising the compassion shown by Alex.
One Facebook user wrote: "A six-year-old who has more humanity, love, and understanding than most adults. Kudos to his parents and I know the world will see more great things coming from Alex."
Another added: "I heard this earlier today, as read by my president. Even with that pre-conditioning, made me cry while reading it just now. Neither of these sweet little boys, someone's sons, are Skittles."
The generous offer from Alex comes as Syria, South Sudan, Afghanistan and Somalia have each produced more than 1 million refugees due to ongoing crises, according to the UN. Earlier this year, the world body's refugee agency said that the number of refugees and displaced people worldwide had surpassed 60 million for the first time.