The ads broadcast on Mexican television, during soccer games and prime time viewing hours, show Kristi Noem, the homeland security secretary, blaming migrants for violent crime and drug trafficking in the United States as she delivers a blunt warning: “We will hunt you down.”

For Mexico’s president, Claudia Sheinbaum, who has yielded to one demand after another from President Trump in a bid to avert or lessen tariffs, Ms. Noem’s appearances on Mexico’s television screens amount to a line in the sand.

Ms. Sheinbaum hit back by calling Ms. Noem’s ads “discriminatory” on Monday and asking Mexican broadcasters to remove them. She went further on Tuesday, saying she will ask Mexico’s Congress to approve a measure to ban such ads from ever appearing again in Mexico.

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“We are going to change the law to prohibit foreign governments from carrying out political and ideological propaganda in our country,” Ms. Sheinbaum said during her daily news conference.

The pushback from Ms. Sheinbaum points to the limits to what her government is willing to accept from the Trump administration as she responds to Mr. Trump’s tariffs, which are already taking a toll on Mexico’s export-driven economy, and his threats to take unilateral military action within Mexico against drug cartels.

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