BRUSSELS—The international aid organization Doctors Without Borders has decided to refuse all future European Union funding as it protests the bloc’s recent migrant deal with Turkey.

The decision follows a May 13 open letter from the group that called the agreement, under which people arriving on Greek islands are to be returned to Turkey, an “historic abdication of [the EU’s] moral and legal responsibilities.” It also described the official welcome offered by Europe to those stranded in Greece as “shameful.”

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