LONDON — In Kuwait, the Muslim Brotherhood is vocally pro-American.

In Iraq, the Brotherhood’s political party has steadfastly supported the American-backed political process and still forms part of the governing coalition.

And in Yemen, the Brotherhood-linked party is cooperating with some of America’s closest Arab allies in a war against a faction backed by Iran.

President Trump’s proposal to designate the Muslim Brotherhood as a terrorist organization raises the difficult question of just whom he intends to target. The original Islamist organization, founded in Egypt in 1928, has spun off or inspired thousands of independent social or political groups around the world, and they are far from monolithic.

They include mainstream associations and advocacy groups in Europe and North America, as well as recognized political parties in United States allies from Morocco to Indonesia. Although most of the Brotherhood-linked parties are sharply critical of United States foreign policy, at least a few — like those in Kuwait, Iraq and Yemen — have sometimes also supported American goals.