The Al Qaeda-affiliated Shebab use an excerpt from Trump's December 7 speech to try and woo Muslims in the West to wage jihad, the SITE Intelligence Group reported.
In his speech, Trump proposed a "total and complete shutdown" on Muslims entering the US until the US was "able to determine and understand this problem" of Islamist violence, following the killing of 14 people by a radicalised couple in California.
Al-Awlaki, who Washington alleges was a senior Al Qaeda operative, was killed by a US drone strike in Yemen in September 2011.
The video, which lasts more than 50 minutes, specifically targets black youths, urging them to convert to Islam and leave for the Somali battlefield using footage of Malcolm X, protests against police actions, and speeches of white supremacists, SITE said.
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It portrays America as a country hostile to its Muslim population, with the narrator claiming that "in the United States, basic human rights and concepts such as justice, tolerance, and the rule of law do not apply if you are a Muslim".
During a Democratic debate last month, Clinton accused Trump of being "ISIS's best recruiter," referring to the self-described Islamic State group, and said the radical jihadists were "going to people showing videos of Donald Trump insulting Islam and Muslims in order to recruit more radical jihadists."
Trump hit back, accusing her of lying, but Clinton's spokeswoman insisted that his remarks were "being used in social media by ISIS as propaganda... To help recruiting," sourcing the information to groups that monitor IS's online activities.