Federal prosecutors are weighing bringing child-pornography charges against former Rep. Anthony Weiner over sexually explicit exchanges he allegedly had with a 15-year-old girl, according to people familiar with the matter.

Mr. Weiner, a New York Democrat, is being investigated by the U.S. attorney’s office in Manhattan and the Federal Bureau of Investigation, which seized his electronic devices, including a laptop and a cellphone, as part of the probe.

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