The states, all led by Democratic attorneys general, joined Washington, D.C., in filing the lawsuit in U.S. District Court in Seattle on Tuesday. It's the first legal challenge by states over the practice.
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Immigration authorities have separated about 2,300 children from their parents in recent weeks, sparking global outrage as images of weeping children emerged.
The president last week issued an executive order designed to end the practice, but the states say his order is riddled with caveats and fails to reunite parents and children who have already been torn apart.
The lawsuit says the migrants have been denied due process and their right to seek asylum.
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