The Prime Minister said United Kingdom authorities were "urgently looking into reports" that the child, who has dual British nationality, is missing.
She said she kneeled down to shield their son, 6, and daughter, 7 months, from the sight.
The Irish boy, Nathaniel, was travelling with his parents Norman and Pederlita Putot, and sister Pearl to celebrate his birthday.
But national broadcaster RTÉ, quoting the Philippine embassy in Madrid, named the family as Norman and Pederlita Putot, and their children Nathaniel and Pearl.
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"Julian is 7 years old and was out with Jom and they were separated".
The father was also hurt but his injuries were not life-threatening.
"We're urgently looking into reports of a child believed missing, who is a British dual national", Xinhua news agency quoted the Prime Minister as saying.
His mother Jom Cadman is in hospital as she recovers from her injuries.
The family, who now live in Australia, are said to have been visiting Barcelona for a wedding. "Terrorism is the great threat that we all face but together we will defeat it".
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Senior lawyer Kapil Sibal , appearing for Jahan, objected to the Supreme Court's decision of handing over the probe to the NIA. The bench drew parallels with the controversial online game 'Blue Whale Challenge' to convey its apprehensions in the matter.
The foreign affairs minister, Julie Bishop, has said one Australian is missing and four others have been injured in the attack.
Julian's mother, Jom, has since been found in hospital in a serious but stable condition.
Eight Australians in total have been affected by attack in the capital of Spain's Catalonia region, that has been claimed by Islamic State, including three who required consular support.
Bruno Gulotta, 35, was reported by Italian media to have been with his wife and two young children when he was struck by the van.
Multiple Taiwanese media reports said two people who were part of a tour group had been injured and were being treated in hospital. Italian officials said Russo's girlfriend suffered fractures and remains hospitalized.
At least 24 different nationalities were among those killed and injured in the horrific attack.
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The Congressional Budget Office said Tuesday that ending the payments next year would cause rates to soar 20% in 2018. The cost-sharing reductions ( CSRs ) help low-to-moderate income individuals purchase health insurance .