The 18-month-old child who was in the car during a chase near the White House was not injured and has been placed with child protective services.
NBC News cites law enforcement sources as saying that the child is believed to be the driver's daughter.
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The announcement came a day after a famine was declared in two areas of South Sudan following three years of civil war and severe inflation.
It is unclear what their alleged plans were.
Anti-terror police are currently questioning the men who were arrested at three separate locations in France.