Trump's tweet said the man killed "most likely would have taken the top spot - Now he is also Dead!"
It was unclear whether the man killed was Abul-Hasan Al-Muhajir, al-Baghdadi's top aide.
Kurdish-led Syrian Democratic Forces (SDF) and US troops were targeting him in the town of Ain al-Beida in the countryside of Jarabulus, the head of the Syrian Observatory for Human Rights told dpa at the weekend.
SDF Commander Mazloum Abdi tweeted then that Al-Muhajir was targeted near Jarabulus as part of operations to chase out Islamic State leaders.
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