Abdullah, the son of the blind Sheikh Omar Abdel-Rahman, writes to request the US release his father, who has been serving a life sentence for allegedly planning the 1993 World Trade Centre attack in New York.
In the press statement released in Arabic on Saturday, Abdullah says: "The American administration's arrogance and stubbornness towards one of the Muslim world's scholars, Sheikh Omar Abdel-Rahman, is putting the lives of its people at risk and costing them a lot."
Abdullah goes on to justify violent attacks and the kidnapping of Americans by Islamist militants, such as Al-Qaeda, explaining that it is the US administration's treatment of his father that "has pushed the Muslim youth to anger for the cleric."
The murder of US ambassador Christopher Stevens to Libya in September during an attack by unknown armed men on the consulate in the city of Benghazi is one example Abdullah cites.
The attack on the US consulate in Libya took place on 11 September 2012 in the wake of massive, world-wide protests organised by Islamists to denounce a US-made film mocking the Prophet Mohamed.
Abdullah warns in his statement that although his family has chosen to protest peacefully others have seen that "the arrogance of the US is not to be dealt with in any other way except through violence and the killing of Americans."
The Sheikh's family, he claims, had demonstrated peacefully and held sit-ins at the US embassy in Cairo for almost 16 months.
"We had already warned the US from the anger of the Muslim world," reads his statement.
"We hope that the US understands the Muslim world's psyche, especially towards its Islamic scholars."
"We further hope that the US responds to President Mohamed Morsi's request to release Omar Abdel-Rahman during his coming trip to the US," Abdullah adds.
Morsi, who is expected to visit the US before the end of March, vowed during his presidential campaign to pressure for the release of Sheikh Omar Abdel-Rahman.
During his campaign Morsi called Abdel Rahman's case a "responsibility on his shoulders" and that he would lobby for his release.
On 8 January, Morsi again repeated his promise during a recent interview with CNN where he stated that he planned to raise the issue of the jailed Sheikh with his American counterpart during his coming visit to the US.
Abdel Rahman is considered the spiritual leader of the radical Gama'a Al-Islamiya group.