Egyptian President Abdel Fattah el-Sisi reportedly made the request to President Trump during his recent trip to Washington.
Placing the Muslim Brotherhood on Washington's list of foreign terrorist organizations would make it a crime for any American to assist the group and would ban from the United States its members, who are active in political parties in several countries.
The White House previously considered designating the Muslim Brotherhood a foreign terrorist organization during Trump's first few weeks in February, 2017, according to The New York Times.
Designating the Muslim Brotherhood a terrorist organization could complicate Washington's relationship with North Atlantic Treaty Organisation ally Turkey.
However, the Pentagon, career national security staff, government lawyers and diplomatic officials have voiced legal and policy objections, and have been scrambling to find a more limited step that would satisfy the White House.
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John R. Bolton, the national security adviser, and Mike Pompeo, the secretary of state, support the idea, officials said.
The Muslim Brotherhood claims a membership of up to one million people. The organization has close ties with President Tayyip Erdogan's ruling AK Party and many of its members fled to Turkey after it was banned in Egypt. Egypt's President Abdel-Fattah el-Sissi came to power in 2014 after removing his predecessor, Mohammed Morsi, who came from the Muslim Brotherhood.
Trump adviser Kellyanne Conway told reporters Tuesday that a designation wouldn't create any diplomatic complications for the administration.
Jonathan Schanzer, senior vice president for the Foundation for Defense of Democracies, which generally backs hawkish policies in the Middle East, doubted that the whole Muslim Brotherhood could be declared a terrorist group under normal processes.
Daniel Benjamin, former State Department coordinator for counterterrorism who now teaches at Dartmouth College, called the move mystifying.
The Brotherhood, founded in Egypt in 1928, says it is a non-violent movement and denies any relationship to violent insurgencies waged by al Qaeda and Islamic State militants.
Turkey is under threat of US sanctions if it pursues plans to purchase Russian S-400 missile defence systems, which are not compatible with North Atlantic Treaty Organisation systems.