Jesús Silva-Herzog, a well-known political analyst, was similarly acerbic in his reaction.

“The Aztec Eagle to Kushner? Really? That is how the government of indignity bids farewell,” he said on Twitter. “A perfect crowning to its indecency.”

The debate spilled into morning television on Wednesday, when Foreign Minister Luis Videgaray spoke by phone to a popular news program to defend the decision.

“Without any doubt, we would not have a free trade treaty today with the United States and Canada without the participation of Jared Kushner,” said Mr. Videgaray, who has formed a close working relationship with the president’s son-in-law.

Mr. Kushner, he said, had managed to intervene in “moments of great uncertainty” to persuade Mr. Trump not to renounce the existing free-trade agreement among the three countries, as the American president had repeatedly threatened, and instead renegotiate it.

In Washington, White House officials, frustrated by the criticism surrounding the award, tried to draw a line between the work Mr. Kushner had done to establish better trade relations and the disparaging words his father-in-law has used to describe the Mexican people. But officials did not initially respond to requests for a public comment about the honor. Instead, a White House official who spoke on the condition of anonymity said: “Jared is very honored to receive this award. A lot of the work that he does is behind the scenes. He keeps his head down on trying to achieve the best outcome for the United States and its partners.”