Envoy Kushner was summoned to the State Department after the Trump administration responded to the high-profile case of a French right-wing activist who was beaten to death in Lyon on February 12.
The assault took place at a left-wing demonstration in the city, where far-right groups carried out counter-protests.
The dispute between the US and France was exacerbated by Kushner's refusal to appear at the French Foreign Ministry - which is seen as diplomatic custom.
Foreign Minister Jean-Noël Barrot's staff confirms that Kushner called and promised that he would not comment on domestic issues in France.
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